Keyword

model categories

Description: A structure in category theory equipped with classes of weak equivalences, fibrations, and cofibrations for studying homotopy theory.

Primary topic: Homotopy and Cohomology in Algebraic Topology (85%)

Wikidata ID: wiki/Q1941896

OpenAlex ID: keywords/model-categories

Model Categories and Their Localizations

2009 · Philip Hirschhorn · Mathematical surveys and monographs · 1,150

Homotopical Algebra

1967 · Daniel G. Quillen · Lecture notes in mathematics · 920

Homotopy Theories and Model Categories

1995 · W.G. Dwyer, J. Spalinski · Elsevier eBooks · 491

Model Categories of Diagram Spectra

2001 · M. A. Mandell, J. P. May, et al. · Proceedings of the London Mathematical Society · 439

A model for the homotopy theory of homotopy theory

2000 · Charles Rezk · Transactions of the American Mathematical Society · 385

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Accessible Categories: The Foundations of Categorical Model Theory

1989 · Michael Makkai, Robert Paré · Contemporary mathematics - American Mathematical Society · 339

Categorical Homotopy Theory

2014 · Emily Riehl · Cambridge University Press eBooks · 324

Spectra and symmetric spectra in general model categories

2001 · Mark Hovey · Journal of Pure and Applied Algebra · 307

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Function complexes in homotopical algebra

1980 · W.G. Dwyer, D.M. Kan · Topology · 295

Simplicial localizations of categories

1980 · W.G. Dwyer, D.M. Kan · Journal of Pure and Applied Algebra · 266

Homotopy Theoretic Models of Identity Types

2009 · Awodey, Steven, Warren, Michael A. · Figshare · 223

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Calculating simplicial localizations

1980 · W.G. Dwyer, D.M. Kan · Journal of Pure and Applied Algebra · 219

Handbook of Algebraic Topology

1995 · Elsevier eBooks · 197

Homotopy Limit Functors on Model Categories and Homotopical Categories

2005 · William Dwyer, Philip Hirschhorn, et al. · Mathematical surveys and monographs · 195

Universal Homotopy Theories

2001 · Daniel Dugger · Advances in Mathematics · 179

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Homotopy limits and colimits

1973 · Rainer M. Vogt · Mathematische Zeitschrift · 167

A cartesian presentation of weakn–categories

2010 · Charles Rezk · Geometry & Topology · 153

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Simplicial presheaves

1987 · J.F. Jardine · Journal of Pure and Applied Algebra · 142

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Homotopy theoretic models of identity types

2008 · STEVE AWODEY, MICHAEL A. WARREN · Mathematical Proceedings of the Cambridge Philosophical Society · 136

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Unifying derived deformation theories

2009 · J.P. Pridham · Advances in Mathematics · 130

Model category structures on chain complexes of sheaves

2001 · Mark Hovey · Transactions of the American Mathematical Society · 118

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Dendroidal sets

2007 · Ieke Moerdijk, Ittay Weiss · Algebraic & Geometric Topology · 117

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More Concise Algebraic Topology

2011 · J. P. May, K. Ponto · University of Chicago Press eBooks · 113

Homotopy theory in general categories

1961 · Peter J. Huber · Mathematische Annalen · 111

Replacing model categories with simplicial ones

2001 · Daniel Dugger · Transactions of the American Mathematical Society · 110

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Works count: 1,095

Citation count: 13,500