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@book{quillen,
author = {Quillen, Daniel G.},
publisher = {Springer-Verlag},
series = {Lecture Notes in Mathematics},
title = {Homotopical Algebra},
volume = 43,
year = 1967
}
@book{hovey,
title={Model Categories},
author={Hovey, M.},
series={Mathematical Surveys and Monographs},
year={1999},
publisher={American Mathematical Society}
}
@book{hirschhorn,
title={Model Categories and Their Localizations},
author={Hirschhorn, P.S.},
series={Mathematical Surveys and Monographs},
year={2009},
publisher={Amer Mathematical Society}
}
@article{jardine,
author = "Jardine, J. F.",
fjournal = "Homology, Homotopy and Applications",
journal = "Homology Homotopy Appl.",
number = "1",
pages = "71--144",
publisher = "International Press of Boston",
title = "Categorical homotopy theory",
url = "http://projecteuclid.org/euclid.hha/1140012467",
volume = "8",
year = "2006"
}
@article{bergner,
author = "Bergner, J.",
journal = "Transactions of the American Mathematical Society",
volume = "359",
pages = "2043-2058",
year = "2007",
month = "May"
}
@article{cisinski,
title = "Théories homotopiques dans les topos ",
journal = "Journal of Pure and Applied Algebra ",
volume = "174",
number = "1",
pages = "43 - 82",
year = "2002",
note = "",
issn = "0022-4049",
doi = "http://dx.doi.org/10.1016/S0022-4049(01)00176-1",
url = "http://www.sciencedirect.com/science/article/pii/S0022404901001761",
author = "Denis-Charles Cisinski",
}
@article{cisinski-presheaf,
title = {{Les pr{\'e}faisceaux comme mod{\`e}les des types d'homotopie}},
author = {Cisinski, Denis-Charles},
url = {https://hal.archives-ouvertes.fr/hal-00440913},
journal = {{Asterisque}},
publisher = {{Soci{\'e}t{\'e} Math{\'e}matique de France}},
volume = {308},
pages = {xxiv+392 pages},
year = {2006},
}
@article{cis10b,
author = {Cisinski,Denis-Charles},
title = {Invariance de la {K-Th\'eorie} par \'equivalences d\'eriv\'ees},
journal = {Journal of K-theory: K-theory and its Applications to Algebra, Geometry, and Topology},
volume = {6},
issue = {03},
month = {12},
month = {12},
year = {2010},
issn = {1865-5394},
pages = {505--546},
numpages = {42},
doi = {10.1017/is009010008jkt094},
URL = {http://journals.cambridge.org/article_S1865243309999809},
}
@article{left-det,
author = {Rosick{\'y}, J. and Tholen, W.},
journal = {Transactions of the American Mathematical Society},
title = {Left-determined model categories and universal homotopy theories},
volume = {355},
pages = {3611-3623},
year = {2003}
}
@book{manes-algebraic-theories,
title = "Algebraic theories",
author = "Manes, Ernest G.",
series = "Graduate texts in mathematics",
publisher = "Springer",
address = "New York, Heidelberg",
url = "http://opac.inria.fr/record=b1080685",
isbn = "3-540-90140-X",
year = 1976
}
@article{brown,
ISSN = {00029947},
URL = {http://www.jstor.org/stable/1996573},
author = {Kenneth S. Brown},
journal = {Transactions of the American Mathematical Society},
pages = {419-458},
publisher = {American Mathematical Society},
title = {Abstract Homotopy Theory and Generalized Sheaf Cohomology},
volume = {186},
year = {1973}
}
@article{szumilo,
author = {{Szumi{\l}o}, K.},
title = "{Two Models for the Homotopy Theory of Cocomplete Homotopy Theories}",
note = {\href {http://arxiv.org/abs/1411.0303} {\path{arXiv:1411.0303}}},
keywords = {Mathematics - Algebraic Topology, Mathematics - Category Theory, 55U35 (Primary), 18G55 (Secondary)},
year = 2014,
month = nov,
}
@article{tt-fibr-cat,
author = {Avigad,Jeremy and Kapulkin,Krzysztof and Lumsdaine,Peter LeFanu},
title = {Homotopy limits in type theory},
journal = {Mathematical Structures in Computer Science},
volume = {25},
issue = {Special Issue 05},
month = {6},
month = {6},
year = {2015},
issn = {1469-8072},
pages = {1040--1070},
numpages = {31},
doi = {10.1017/S0960129514000498},
URL = {http://journals.cambridge.org/article_S0960129514000498},
}
@phdthesis{lumsdaine,
author = {Lumsdaine, Peter~LeFanu},
title = {Higher categories from type theories},
school = {Carnegie Mellon University},
year = 2010
}
@book{baues,
title={Algebraic Homotopy},
author={Baues, H.J.},
isbn={9780521333764},
lccn={86032738},
series={Australian Mathematical Society Lecture Series},
url={http://books.google.ru/books?id=T6RyIBxDC54C},
year={1989},
publisher={Cambridge University Press}
}
@article{folk,
title = {{A folk model structure on omega-cat}},
author = {Lafont, Yves and M{\'e}tayer, Fran{\c c}ois and Worytkiewicz, Krzysztof},
pages = {1183-1231},
journal = {Advances in Mathematics},
volume = {224},
number = {3},
year = {2010},
}
@book{lurie-topos,
title = "Higher topos theory",
author = "Lurie, Jacob",
series = "Annals of mathematics studies",
publisher = "Princeton University Press",
address = "Princeton, N.J., Oxford",
url = "http://opac.inria.fr/record=b1128872",
isbn = "978-0-691-14048-3",
year = 2009
}
@book{lurie-algebra,
title = "Higher algebra",
author = "Lurie, Jacob",
note = "Unpublished"
}
@ARTICLE{kap-lum-voe,
author = {{Kapulkin}, C. and {LeFanu Lumsdaine}, P.},
title = "{The Simplicial Model of Univalent Foundations (after Voevodsky)}",
note = {\href {http://arxiv.org/abs/1211.2851} {\path{arXiv:1211.2851}}},
keywords = {Mathematics - Logic, Mathematics - Algebraic Topology, Mathematics - Category Theory, 03B15, 55U10 (Primary), 18C50, 55U35 (Secondary)},
year = 2012,
month = nov,
}
@ARTICLE{semi-model,
author = {{Spitzweck}, M.},
title = "{Operads, Algebras and Modules in General Model Categories}",
note = {\href {https://arxiv.org/abs/math/0101102} {\path{arXiv:0101102}}},
year = 2001,
month = jan,
}
@ARTICLE{hovey-semi,
author = {{Hovey}, M.},
title = "{Monoidal model categories}",
note = {\href {https://arxiv.org/abs/math/9803002} {\path{arXiv:9803002}}},
year = 1998,
month = feb,
}
@article{barwick-semi,
author = "Barwick, Clark",
fjournal = "Homology, Homotopy and Applications",
journal = "Homology Homotopy Appl.",
number = "2",
pages = "245--320",
publisher = "International Press of Boston",
title = "On left and right model categories and left and right Bousfield localizations",
url = "https://projecteuclid.org:443/euclid.hha/1296223884",
volume = "12",
year = "2010"
}
@ARTICLE{kap-lum-voe-uni,
author = {{Kapulkin}, C. and {LeFanu Lumsdaine}, P. and {Voevodsky}, V.},
title = "{Univalence in Simplicial Sets}",
note = {\href {http://arxiv.org/abs/1203.2553} {\path{arXiv:1203.2553}}},
keywords = {Mathematics - Algebraic Topology, Mathematics - Category Theory, 55U10 (Primary) 55U35 (Secondary)},
year = 2012,
month = mar,
}
@article{shul-inv,
author = {Shulman,Michael},
title = {Univalence for inverse diagrams and homotopy canonicity},
journal = {Mathematical Structures in Computer Science},
volume = {25},
issue = {Special Issue 05},
month = {6},
year = {2015},
issn = {1469-8072},
pages = {1203--1277},
numpages = {75},
doi = {10.1017/S0960129514000565},
URL = {http://journals.cambridge.org/article_S0960129514000565},
}
@article{shul-eleg,
author = {{Shulman}, M.},
title = "{The univalence axiom for elegant Reedy presheaves}",
journal = {Homology, Homotopy and Applications},
volume = {17:2},
pages = {81--106},
year = 2015
}
@ARTICLE{cisinski-eleg,
author = {{Cisinski}, D.-C.},
title = "{Univalent universes for elegant models of homotopy types}",
note = {\href {http://arxiv.org/abs/1406.0058} {\path{arXiv:1406.0058}}},
keywords = {Mathematics - Algebraic Topology, Mathematics - Category Theory, Mathematics - Logic},
year = 2014,
month = may,
}
@InProceedings{cubical-old,
author = {Marc Bezem and Thierry Coquand and Simon Huber},
title = {{A Model of Type Theory in Cubical Sets}},
booktitle = {19th International Conference on Types for Proofs and Programs (TYPES 2013)},
pages = {107--128},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-72-9},
ISSN = {1868-8969},
year = {2014},
volume = {26},
editor = {Ralph Matthes and Aleksy Schubert},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2014/4628},
URN = {urn:nbn:de:0030-drops-46284},
doi = {http://dx.doi.org/10.4230/LIPIcs.TYPES.2013.107},
annote = {Keywords: Models of dependent type theory, cubical sets, Univalent Foundations}
}
@article{cubical-tt,
author = {{Cohen}, Cyril and {Coquand}, Thierry and {Huber}, Simon and {M{\"o}rtberg}, Anders},
title = "{Cubical Type Theory: a constructive interpretation of the univalence axiom}",
note = {\href {http://arxiv.org/abs/1611.02108} {\path{arXiv:1611.02108}}},
keywords = {Computer Science - Logic in Computer Science, Mathematics - Logic, F.3.2, F.4.1},
year = 2016,
month = nov,
}
@inproceedings{circle,
author = {Licata, Daniel R. and Shulman, Michael},
title = {Calculating the Fundamental Group of the Circle in Homotopy Type Theory},
booktitle = {Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science},
series = {LICS '13},
year = {2013},
isbn = {978-0-7695-5020-6},
pages = {223--232},
numpages = {10},
url = {http://dx.doi.org/10.1109/LICS.2013.28},
doi = {10.1109/LICS.2013.28},
acmid = {2591407},
publisher = {IEEE Computer Society},
address = {Washington, DC, USA},
}
@incollection {MLTT72,
AUTHOR = {Martin-L{\"o}f, Per},
TITLE = {An intuitionistic theory of types},
BOOKTITLE = {Twenty-five years of constructive type theory ({V}enice,
1995)},
SERIES = {Oxford Logic Guides},
VOLUME = {36},
PAGES = {127--172},
PUBLISHER = {Oxford Univ. Press, New York},
YEAR = {1998},
MRCLASS = {03B15 (03F55)},
MRNUMBER = {1686864},
}
@incollection{MLTT73,
AUTHOR = {Martin-L{\"o}f, Per},
TITLE = {An intuitionistic theory of types: predicative part},
BOOKTITLE = {Logic {C}olloquium '73 ({B}ristol, 1973)},
PAGES = {73--118. Studies in Logic and the Foundations of Mathematics,
Vol. 80},
PUBLISHER = {North-Holland, Amsterdam},
YEAR = {1975},
MRCLASS = {02C15 (02D99)},
MRNUMBER = {0387009 (52 \#7856)},
MRREVIEWER = {Horst Luckhardt},
}
@incollection{MLTT79,
AUTHOR = {Martin-L{\"o}f, Per},
TITLE = {Constructive mathematics and computer programming},
BOOKTITLE = {Logic, methodology and philosophy of science, {VI}
({H}annover, 1979)},
SERIES = {Stud. Logic Found. Math.},
VOLUME = {104},
PAGES = {153--175},
PUBLISHER = {North-Holland, Amsterdam},
YEAR = {1982},
MRCLASS = {03F50 (03B70 03F55 68Q45)},
MRNUMBER = {682410 (85d:03112)},
MRREVIEWER = {B. H. Mayoh},
DOI = {10.1016/S0049-237X(09)70189-2},
URL = {http://dx.doi.org/10.1016/S0049-237X(09)70189-2},
}
@book{MLTT-bibliopolis,
AUTHOR = {Martin-L{\"o}f, Per},
TITLE = {Intuitionistic type theory},
SERIES = {Studies in Proof Theory. Lecture Notes},
VOLUME = {1},
NOTE = {Notes by Giovanni Sambin},
PUBLISHER = {Bibliopolis, Naples},
YEAR = {1984},
PAGES = {iv+91},
ISBN = {88-7088-105-9},
MRCLASS = {03B15 (03F50 03F55)},
MRNUMBER = {769301 (86j:03005)},
MRREVIEWER = {M. M. Richter},
}
@article{CoC,
title = "The calculus of constructions",
journal = "Information and Computation",
volume = "76",
number = "2",
pages = "95 - 120",
year = "1988",
note = "",
issn = "0890-5401",
doi = "http://dx.doi.org/10.1016/0890-5401(88)90005-3",
url = "http://www.sciencedirect.com/science/article/pii/0890540188900053",
author = "Thierry Coquand and G{\'e}rard Huet",
abstract = ""
}
@incollection{howard,
author = {Howard, William A.},
booktitle = {To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus, and Formalism},
citeulike-article-id = {5917448},
comment = {Reprint of 1969 article},
editor = {Seldin, J. P. and Hindley, J. R.},
keywords = {dissertation},
pages = {479--490},
posted-at = {2009-10-09 20:21:48},
priority = {0},
publisher = {Academic Press},
title = {{The formulas-as-types notion of construction}},
year = {1980}
}
@inproceedings{seely,
author = {R. A. G. Seely},
title = {Locally cartesian closed categories and type theory},
booktitle = {Math. Proc. Camb. Phil. Soc.},
pages = {33–48},
year = {1984}
}
@inproceedings{hofmann,
author = {Martin Hofmann},
title = {On the Interpretation of Type Theory in Locally Cartesian Closed Categories},
booktitle = {Proceedings of Computer Science Logic, Lecture Notes in Computer Science},
year = {1994},
pages = {427--441},
publisher = {Springer}
}
@Inbook{ext-eq,
author="Clairambault, Pierre and Dybjer, Peter",
editor="Ong, Luke",
title="The Biequivalence of Locally Cartesian Closed Categories and Martin-L{\"o}f Type Theories",
bookTitle="Typed Lambda Calculi and Applications: 10th International Conference, TLCA 2011, Novi Sad, Serbia, June 1-3, 2011. Proceedings",
year="2011",
publisher="Springer Berlin Heidelberg",
address="Berlin, Heidelberg",
pages="91--106",
isbn="978-3-642-21691-6",
doi="10.1007/978-3-642-21691-6_10",
url="http://dx.doi.org/10.1007/978-3-642-21691-6_10"
}
@Inbook{cwf,
author="Dybjer, Peter",
editor="Berardi, Stefano
and Coppo, Mario",
title="Internal type theory",
bookTitle="Types for Proofs and Programs: International Workshop, TYPES '95 Torino, Italy, June 5--8, 1995 Selected Papers",
year="1996",
publisher="Springer Berlin Heidelberg",
address="Berlin, Heidelberg",
pages="120--134",
isbn="978-3-540-70722-6",
doi="10.1007/3-540-61780-9_66",
url="http://dx.doi.org/10.1007/3-540-61780-9_66"
}
@inproceedings{wadler,
author = {Philip Wadler},
title = {Theorems for free!},
booktitle = {Functional Programming Languages and Computer Architecture},
year = {1989},
pages = {347--359},
publisher = {ACM Press}
}
@article{induction-recursion,
author = {Peter Dybjer},
title = {A General Formulation of Simultaneous Inductive-Recursive Definitions in Type Theory},
journal = {Journal of Symbolic Logic},
year = {1998},
volume = {65},
pages = {2000}
}
@inproceedings{without-k,
author = {Cockx, Jesper and Devriese, Dominique and Piessens, Frank},
title = {Pattern Matching Without {K}},
booktitle = {Proceedings of the 19th ACM SIGPLAN International Conference on Functional Programming},
series = {ICFP '14},
year = {2014},
isbn = {978-1-4503-2873-9},
location = {Gothenburg, Sweden},
pages = {257--268},
numpages = {12},
url = {http://doi.acm.org/10.1145/2628136.2628139},
doi = {10.1145/2628136.2628139},
acmid = {2628139},
publisher = {ACM},
address = {New York, NY, USA},
keywords = {agda, dependent pattern matching, homotopy type theory, k axiom},
}
@Book{hottbook,
author = {The {Univalent Foundations Program}},
title = {Homotopy Type Theory: Univalent Foundations of Mathematics},
publisher = {\url{https://homotopytypetheory.org/book}},
address = {Institute for Advanced Study},
year = 2013
}
@inproceedings{groupoid,
author = {Martin Hofmann and Thomas Streicher},
title = {The Groupoid Interpretation of Type Theory},
booktitle = {In Venice Festschrift},
year = {1996},
pages = {83--111},
publisher = {Oxford University Press}
}
@article{awodey,
author = {{Awodey}, S.},
title = "{Type theory and homotopy}",
note = {\href {http://arxiv.org/abs/1010.1810} {\path{arXiv:1010.1810}}},
keywords = {Mathematics - Category Theory, Mathematics - Logic, 18G55},
year = 2010,
month = oct,
}
@article{warren,
author = {{Awodey}, S. and {Warren}, M.~A.},
title = "{Homotopy theoretic models of identity types}",
note = {\href {http://arxiv.org/abs/0709.0248} {\path{arXiv:0709.0248}}},
keywords = {Mathematics - Logic, Mathematics - Algebraic Topology, Mathematics - Category Theory, 18C50 (Primary), 18G55, 03B15, 03F65 (Secondary)},
year = 2007,
month = sep,
}
@article{cubical,
author = {{Bezem}, Marc and {Coquand}, Thierry and {Huber}, Simon},
title = "{A model of type theory in cubical sets}",
year = 2014
}
@book{luo94,
author = "Zhaohui Luo",
title = "{C}omputation and {R}easoning: {A} {T}ype {T}heory for {C}omputer {S}cience",
publisher = "{O}xford {U}niversity {P}ress",
year = "1994"
}
@InCollection{pitts,
author = {A. M. Pitts},
title = {Categorical Logic},
booktitle = {Handbook of Logic in Computer Science, Volume
5. Algebraic and Logical Structures},
publisher = {Oxford University Press},
year = 2000,
pages = {39--128},
chapter = 2,
editor = {S. Abramsky and D. M. Gabbay and T. S. E. Maibaum},
isbn = {0-19-853781-6},
url = {http://www.oup.co.uk/isbn/0-19-853781-6}
}
@book{streicher,
author = {Streicher, Thomas},
title = {Semantics of Type Theory: Correctness, Completeness, and Independence Results},
year = {1991},
isbn = {0-8176-3594-7},
publisher = {Birkhauser Boston Inc.},
address = {Cambridge, MA, USA},
}
@article{GAT,
title = "Generalised algebraic theories and contextual categories ",
journal = "Annals of Pure and Applied Logic ",
volume = "32",
number = "",
pages = "209 - 243",
year = "1986",
note = "",
issn = "0168-0072",
doi = "http://dx.doi.org/10.1016/0168-0072(86)90053-9",
url = "http://www.sciencedirect.com/science/article/pii/0168007286900539",
author = "John Cartmell"
}
@article{EAT,
year={1999},
issn={0002-5240},
journal={algebra universalis},
volume={41},
number={3},
doi={10.1007/s000120050111},
title={On essentially algebraic theories and their generalizations},
url={http://dx.doi.org/10.1007/s000120050111},
publisher={Birkhäuser Verlag},
author={Adámek, J. and Hébert, M. and Rosick{\'y}, J.},
pages={213-227},
}
@book{LPC,
author = "J. Ad{\'a}mek and J. Rosick{\'y}",
title = {Locally Presentable and Accessible Categories},
publisher = {Cambridge University Press},
year = {1994},
isbn = {9780511600579},
url = {http://dx.doi.org/10.1017/CBO9780511600579}
}
@article{monad-equational-presentation,
title = "Adjunctions whose counits are coequalizers, and presentations of finitary enriched monads ",
journal = "Journal of Pure and Applied Algebra ",
volume = "89",
number = "1–2",
pages = "163 - 179",
year = "1993",
note = "",
issn = "0022-4049",
doi = "http://dx.doi.org/10.1016/0022-4049(93)90092-8",
url = "http://www.sciencedirect.com/science/article/pii/0022404993900928",
author = "G.M. Kelly and A.J. Power",
abstract = "A right adjoint functor is said to be of descent type if the counit of the adjunction is pointwise a coequalizer. Building on the results of Tholen's doctoral thesis, we give necessary and sufficient conditions for a composite to be of descent type when each factor is so. We apply this to show that every finitary monad on a locally-finitely-presentable enriched category A admits a presentation in terms of basic operations and equations between derived operations, the arties here being the finitely-presentable objects of A. "
}
@article{b-systems,
author = {{Voevodsky}, V.},
title = "{B-systems}",
note = {\href {http://arxiv.org/abs/1410.5389} {\path{arXiv:1410.5389}}},
keywords = {Mathematics - Logic, Mathematics - Category Theory, 03B15, 03B22, 03F50, 03G25},
year = 2014,
month = oct,
}
@article{c-systems,
author = {{Voevodsky}, V.},
title = "{Subsystems and regular quotients of C-systems}",
note = {\href {http://arxiv.org/abs/1406.7413} {\path{arXiv:1406.7413}}},
keywords = {Mathematics - Logic, 03B15, 03B22, 03F50, 03G25},
year = 2014,
month = jun,
}
@article{c-systems-monad,
author = {{Voevodsky}, V.},
title = "{C-system of a module over a monad on sets}",
note = {\href {http://arxiv.org/abs/1407.3394} {\path{arXiv:1407.3394}}},
keywords = {Mathematics - Logic, 03B15, 03B22, 03F50, 03G25},
year = 2014,
month = jul,
}
@article{PHL,
title = "Partial Horn logic and cartesian categories ",
journal = "Annals of Pure and Applied Logic ",
volume = "145",
number = "3",
pages = "314 - 353",
year = "2007",
note = "",
issn = "0168-0072",
doi = "http://dx.doi.org/10.1016/j.apal.2006.10.001",
url = "http://www.sciencedirect.com/science/article/pii/S0168007206001229",
author = "E. Palmgren and S.J. Vickers",
keywords = "Cartesian theory",
keywords = "Essentially algebraic",
keywords = "Free algebra",
keywords = "Classifying category",
keywords = "Syntactic category",
keywords = "Partial algebra "
}
@book{elephant,
title = "Sketches of an elephant : a topos theory compendium",
author = "Johnstone, Peter T.",
series = "Oxford Logic Guides",
publisher = "Clarendon Press",
address = "Oxford",
url = "http://opac.inria.fr/record=b1107183",
isbn = "0-19-853425-6",
note = "Autre tirage : 2008",
year = 2002
}
@article{local-universes,
author = {Lumsdaine, Peter Lefanu and Warren, Michael A.},
title = {The Local Universes Model: An Overlooked Coherence Construction for Dependent Type Theories},
journal = {ACM Trans. Comput. Logic},
issue_date = {July 2015},
volume = {16},
number = {3},
month = jul,
year = {2015},
issn = {1529-3785},
pages = {23:1--23:31},
articleno = {23},
numpages = {31},
url = {http://doi.acm.org/10.1145/2754931},
doi = {10.1145/2754931},
acmid = {2754931},
publisher = {ACM},
address = {New York, NY, USA},
keywords = {Categorical semantics, coherence theorems, comprehension categories, dependent type theory},
}
@article{kapulkin,
author = {{Kapulkin}, C.},
title = "{Locally Cartesian Closed Quasicategories from Type Theory}",
note = {\href {http://arxiv.org/abs/1507.02648} {\path{arXiv:1507.02648}}},
keywords = {Mathematics - Category Theory, Mathematics - Algebraic Topology, Mathematics - Logic, Primary: 18G55, Secondary: 03B70, 55U35},
year = 2015,
month = jul,
}
@article{kapulkin-szumilo,
author = {{Kapulkin}, C. and {Szumi{\l}o}, K.},
title = "{Quasicategories of Frames of Cofibration Categories}",
note = {\href {http://arxiv.org/abs/1506.08681} {\path{arXiv:1506.08681}}},
keywords = {Mathematics - Algebraic Topology, Mathematics - Category Theory, Primary: 55U35, Secondary: 18G55, 55U40},
year = 2015,
month = jun,
}
@article{kapulkin-szumilo-fin-comp,
author = {{Kapulkin}, C. and {Szumi{\l}o}, K.},
title = "{Internal Language of Finitely Complete $(\infty, 1)$-categories}",
note = {\href {http://arxiv.org/abs/1709.09519} {\path{arXiv:1709.09519}}},
year = 2017,
month = sep,
}
@article{alg-tt,
author = {{Isaev}, V.},
title = "{Algebraic Presentations of Dependent Type Theories}",
note = {\href {http://arxiv.org/abs/1602.08504} {\path{arXiv:1602.08504}}},
year = 2016,
month = feb,
}
@article{f-model-structures,
author = {{Isaev}, V.},
year = {2018},
month = {01},
pages = {43-66},
title = {On fibrant objects in model categories},
volume = {33},
journal = {Theory and Applications of Categories}
}
article{alg-models,
author = {{Isaev}, V.},
title = "Model Structures on Categories of Models of Type Theories",
note = {\href {http://arxiv.org/abs/1607.07407} {\path{arXiv:1607.07407}}},
keywords = {Mathematics - Category Theory},
year = 2016,
month = jul,
}
@article{alg-models,
author = {{Isaev}, V.},
title = {Model structures on categories of models of type theories},
journal = {Mathematical Structures in Computer Science},
publisher = {Cambridge University Press},
year = {2017},
pages = {1--28}
}
@article{marked-obj,
author = {{Isaev}, V.},
title = "Model category of marked objects",
note = {\href {http://arxiv.org/abs/1610.08459} {\path{arXiv:1610.08459}}},
keywords = {Mathematics - Category Theory},
year = 2016,
month = oct,
}
@article{morita-equiv,
author = {{Isaev}, V.},
title = "{Morita equivalences between algebraic dependent type theories}",
year = "2018",
month = "Apr",
eprint = {1804.05045},
note = {\href {http://arxiv.org/abs/1804.05045} {\path{arXiv:1804.05045}}},
}
@unpublished{Joyal,
author = "{Joyal}, A.",
title = "Theory of quasi-categories {I}",
note = "unpublished",
}
@unpublished{semi-smith,
author = "{Batanin}, M. and {White}, D.",
title = "Left Bousfield localization without left properness",
note = "unpublished",
}
@ARTICLE{kap-lum-model,
author = {{Kapulkin}, C. and {LeFanu Lumsdaine}, P.},
title = "{The homotopy theory of type theories}",
note = {\href {http://arxiv.org/abs/1610.00037} {\path{arXiv:1610.00037}}},
keywords = {Mathematics - Category Theory, 03B15, 18G55 (primary), 55U35, 18C50},
year = 2016,
month = sep,
}
@book{Terese,
title={Term Rewriting Systems},
author={Terese},
isbn={9780521391153},
series={Cambridge Tracts in Theoretical Computer Science},
year={2003},
publisher={Cambridge University Press}
}
@article{vogt-we,
author = {Vogt, R.~M.},
title = "{The HELP-Lemma And Its Converse In Quillen Model Categories}",
note = {\href {http://arxiv.org/abs/1004.5249} {\path{arXiv:1004.5249}}},
year = 2010,
month = apr,
}
@article{olschok,
author="Olschok, Marc",
title="Left Determined Model Structures for Locally Presentable Categories",
journal="Applied Categorical Structures",
year="2011",
volume="19",
number="6",
pages="901--938",
abstract="We extend a result of Cisinski on the construction of cofibrantly generated model structures from (Grothendieck) toposes to locally presentable categories and from monomorphism to more general cofibrations. As in the original case, under additional conditions, the resulting model structures are ``left determined'' in the sense of Rosick{\'y} and Tholen.",
issn="1572-9095",
doi="10.1007/s10485-009-9207-2",
url="http://dx.doi.org/10.1007/s10485-009-9207-2"
}
@Article{Nikolaus2015,
author="Nikolaus, Thomas and Schreiber, Urs and Stevenson, Danny",
title={Principal $\infty$-bundles: presentations},
journal="Journal of Homotopy and Related Structures",
year="2015",
volume="10",
number="3",
pages="565--622",
issn="1512-2891",
url="http://dx.doi.org/10.1007/s40062-014-0077-4"
}
@article{schreiber-linear,
author = {{Schreiber}, U.},
title = "{Quantization via Linear homotopy types}",
note = {\href {http://arxiv.org/abs/1402.7041} {\path{arXiv:1402.7041}}},
keywords = {Mathematical Physics, High Energy Physics - Theory, Mathematics - Algebraic Topology, Mathematics - Logic, 03-06, 18F99, 19-06, 55-02, 81-02},
year = 2014,
month = feb,
}
@article{algebraic-fibrant-objects,
title = "Algebraic models for higher categories",
journal = "Indagationes Mathematicae",
volume = "21",
number = "1",
pages = "52 - 75",
year = "2011",
issn = "0019-3577",
doi = "https://doi.org/10.1016/j.indag.2010.12.004",
url = "http://www.sciencedirect.com/science/article/pii/S0019357710000133",
author = "Thomas Nikolaus",
}
@article{Dwyer1980,
title = "Calculating simplicial localizations",
journal = "Journal of Pure and Applied Algebra",
volume = "18",
number = "1",
pages = "17 - 35",
year = "1980",
note = "",
issn = "0022-4049",
doi = "http://dx.doi.org/10.1016/0022-4049(80)90113-9",
url = "http://www.sciencedirect.com/science/article/pii/0022404980901139",
author = "W.G. Dwyer and D.M. Kan",
}
@incollection{klop-trs,
author = {Klop, J. W.},
chapter = {Term Rewriting Systems},
title = {Handbook of Logic in Computer Science (Vol. 2)},
editor = {Abramsky, S. and Gabbay, Dov M. and Maibaum, S. E.},
year = {1992},
isbn = {0-19-853761-1},
pages = {1--116},
numpages = {116},
url = {http://dl.acm.org/citation.cfm?id=162552.162559},
acmid = {162559},
publisher = {Oxford University Press, Inc.},
address = {New York, NY, USA},
}
@article{toyama,
author = {Toyama, Yoshihito},
title = {On the Church-Rosser Property for the Direct Sum of Term Rewriting Systems},
journal = {J. ACM},
issue_date = {Jan. 1987},
volume = {34},
number = {1},
month = jan,
year = {1987},
issn = {0004-5411},
pages = {128--143},
numpages = {16},
url = {http://doi.acm.org/10.1145/7531.7534},
doi = {10.1145/7531.7534},
acmid = {7534},
publisher = {ACM},
address = {New York, NY, USA},
}
@article{klop-confluence,
author = {Klop, Jan Willem and Middeldorp, Aart and Toyama, Yoshihito and de Vrijer, Roel},
title = {Modularity of Confluence: A Simplified Proof},
journal = {Inf. Process. Lett.},
issue_date = {Jan. 28, 1994},
volume = {49},
number = {2},
month = jan,
year = {1994},
issn = {0020-0190},
pages = {101--109},
numpages = {9},
url = {http://dx.doi.org/10.1016/0020-0190(94)90034-5},
doi = {10.1016/0020-0190(94)90034-5},
acmid = {177268},
publisher = {Elsevier North-Holland, Inc.},
address = {Amsterdam, The Netherlands, The Netherlands},
keywords = {term rewriting systems, theory of computation},
}
@inbook{oostrom-confluence,
author="van Oostrom, Vincent",
editor="Armando, Alessandro
and Baumgartner, Peter
and Dowek, Gilles",
title="Modularity of Confluence",
bookTitle="Automated Reasoning: 4th International Joint Conference, IJCAR 2008 Sydney, Australia, August 12-15, 2008 Proceedings",
year="2008",
publisher="Springer Berlin Heidelberg",
address="Berlin, Heidelberg",
pages="348--363",
abstract="We present a novel proof of Toyama's famous modularity of confluence result for term rewriting systems. Apart from being short and intuitive, the proof is modular itself in that it factors through the decreasing diagrams technique for abstract rewriting systems, is constructive in that it gives a construction for the converging rewrite sequences given a pair of diverging rewrite sequences, and general in that it extends to opaque constructor-sharing term rewriting systems. We show that for term rewrite systems with extra variables, confluence is not preserved under decomposition, and discuss whether for these systems confluence is preserved under composition.",
isbn="978-3-540-71070-7",
doi="10.1007/978-3-540-71070-7_31",
url="https://doi.org/10.1007/978-3-540-71070-7_31"
}
@Inbook{ohlebusch-confluence,
author="Ohlebusch, Enno",
editor="Tison, Sophie",
title="On the modularity of confluence of constructor-sharing term rewriting systems",
bookTitle="Trees in Algebra and Programming --- CAAP'94: 19th International Colloquium Edinburgh, U.K., April 11--13, 1994 Proceedings",
year="1994",
publisher="Springer Berlin Heidelberg",
address="Berlin, Heidelberg",
pages="261--275",
abstract="Toyama's Theorem states that confluence is a modular property of disjoint term rewriting systems. This theorem does not generalize to combined systems with shared constructors. Thus the question arises naturally whether there are sufficient conditions which ensure the modularity of confluence in the presence of shared constructors. In particular, Kurihara and Krishna Rao posed the problem whether there arc interesting sufficient conditions independent of termination. This question appeared as Problem 59 in the list of open problems in the theory of rewriting published recently [DJK93]. The present paper gives an affirmative answer to that question. Among other sufficient criteria, it is shown that confluence is preserved under the combination of constructorsharing systems if the systems arc also normalizing. This in conjunction with the fact that normalization is modular for those systems implies the modularity of semi-completeness.",
isbn="978-3-540-48373-1",
doi="10.1007/BFb0017487",
url="https://doi.org/10.1007/BFb0017487"
}
@article{ohlebusch-composable,
title = "Modular Properties of Composable Term Rewriting Systems",
journal = "Journal of Symbolic Computation",
volume = "20",
number = "1",
pages = "1 - 41",
year = "1995",
issn = "0747-7171",
doi = "https://doi.org/10.1006/jsco.1995.1036",
url = "http://www.sciencedirect.com/science/article/pii/S074771718571036X",
author = "Enno Ohlebusch"
}
@article{middeldorp-completeness,
title = "Completeness of Combinations of Constructor Systems",
journal = "Journal of Symbolic Computation",
volume = "15",
number = "3",
pages = "331 - 348",
year = "1993",
issn = "0747-7171",
doi = "https://doi.org/10.1006/jsco.1993.1024",
url = "http://www.sciencedirect.com/science/article/pii/S0747717183710242",
author = "Aart Middeldorp and Yoshihito Toyama"
}
@article{raoult,
author = {Raoult, Jean-Claude and Vuillemin, Jean},
title = {Operational and Semantic Equivalence Between Recursive Programs},
journal = {J. ACM},
issue_date = {Oct. 1980},
volume = {27},
number = {4},
month = oct,
year = {1980},
issn = {0004-5411},
pages = {772--796},
numpages = {25},
url = {http://doi.acm.org/10.1145/322217.322229},
doi = {10.1145/322217.322229},
acmid = {322229},
publisher = {ACM},
address = {New York, NY, USA},
}