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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorDmitri Pavlov
   • CommentTimeMay 7th 2022
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexCreated: A book by [[Emily Riehl]] and [[Dominic Verity]]. Elements of ∞-category theory. Cambridge Studies in Advanced Mathematics 194. Cambridge University Press, Cambridge, 2022. xix+759 pp. ISBN: 978-1-108-83798-9 ### Frontmatter ### Dedication ### Contents ### Preface ## Part I - Basic ∞-Category Theory ### 1 - ∞-Cosmoi and Their Homotopy 2-Categories ### 2 - Adjunctions, Limits, and Colimits I ### 3 - Comma ∞-Categories ### 4 - Adjunctions, Limits, and Colimits II ### 5 - Fibrations and Yoneda’s Lemma ## An Interlude On ∞-Cosmology ### 6 - Exotic ∞-Cosmoi ## Part II - The Calculus Of Modules ### 7 - Two-Sided Fibrations and Modules ### 8 - The Calculus of Modules ### 9 - Formal ∞-Category Theory in a Virtual Equipment ## Part III - Model Independence ### 10 - Change-of-Model Functors ### 11 - Model Independence ### 12 - Applications of Model Independence ## Appendix of Abstract Nonsense ### Appendix A - Basic Concepts of Enriched Category Theory ### Appendix B - An Introduction to 2-Category Theory ### Appendix C - Abstract Homotopy Theory ## Appendix of Concrete Constructions ### Appendix D - The Combinatorics of (Marked) Simplicial Sets ### Appendix E - ∞-Cosmoi Found in Nature ### Appendix F - The Analytic Theory of Quasi-Categories ### References ### Glossary of Notation ### Index <a href="https://ncatlab.org/nlab/revision/Elements+of+%E2%88%9E-Category+Theory/1">v1</a>, <a href="https://ncatlab.org/nlab/show/Elements+of+%E2%88%9E-Category+Theory">current</a>

   Created:

   A book by Emily Riehl and Dominic Verity.

   Elements of ∞-category theory.

   Cambridge Studies in Advanced Mathematics 194. Cambridge University Press, Cambridge, 2022. xix+759 pp.

   ISBN: 978-1-108-83798-9

   Frontmatter

   Dedication

   Contents

   Preface

   Part I - Basic ∞-Category Theory

   1 - ∞-Cosmoi and Their Homotopy 2-Categories

   2 - Adjunctions, Limits, and Colimits I

   3 - Comma ∞-Categories

   4 - Adjunctions, Limits, and Colimits II

   5 - Fibrations and Yoneda’s Lemma

   An Interlude On ∞-Cosmology

   6 - Exotic ∞-Cosmoi

   Part II - The Calculus Of Modules

   7 - Two-Sided Fibrations and Modules

   8 - The Calculus of Modules

   9 - Formal ∞-Category Theory in a Virtual Equipment

   Part III - Model Independence

   10 - Change-of-Model Functors

   11 - Model Independence

   12 - Applications of Model Independence

   Appendix of Abstract Nonsense

   Appendix A - Basic Concepts of Enriched Category Theory

   Appendix B - An Introduction to 2-Category Theory

   Appendix C - Abstract Homotopy Theory

   Appendix of Concrete Constructions

   Appendix D - The Combinatorics of (Marked) Simplicial Sets

   Appendix E - ∞-Cosmoi Found in Nature

   Appendix F - The Analytic Theory of Quasi-Categories

   References

   Glossary of Notation

   Index

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMay 8th 2022
   • (edited May 8th 2022)
   • PermaLink
   Author: Urs
   Format: MarkdownItextouched the formatting added [doi:10.1017/9781108936880](https://doi.org/10.1017/9781108936880) added [pdf](https://emilyriehl.github.io/files/elements.pdf) added what it's about: > on [[(∞,1)-category theory]] formulated via [[∞-cosmoi]] and the [[homotopy 2-category of (∞,1)-categories]] ([[formal (infinity,1)-category theory|formal $(\infty,1)$-category theory]]). added pointer to related texts: * [[Emily Riehl]], [[Dominic Verity]], _The 2-category theory of quasi-categories_, Advances in Mathematics **280** (2015) 549-642 $[$[arXiv:1306.5144](http://arxiv.org/abs/1306.5144), [doi:10.1016/j.aim.2015.04.021](https://doi.org/10.1016/j.aim.2015.04.021)$]$ * [[Emily Riehl]], [[Dominic Verity]], _Infinity category theory from scratch_, Higher Structures Vol 4, No 1 (2020) $[$[arXiv:1608.05314](https://arxiv.org/abs/1608.05314), [pdf](http://www.math.jhu.edu/~eriehl/scratch.pdf)$]$ * [[Emily Riehl]], *The formal theory of ∞-categories*, talk at *[Categories and Companions Symposium June 8–12, 2021](http://web.science.mq.edu.au/groups/coact/seminar/CaCS2021/)* ([video](https://youtu.be/iX5Fxen3K-U)) added `category:reference`-tag cross-linked back to this new entry form entries that are referencing this book <a href="https://ncatlab.org/nlab/revision/diff/Elements+of+%E2%88%9E-Category+Theory/2">diff</a>, <a href="https://ncatlab.org/nlab/revision/Elements+of+%E2%88%9E-Category+Theory/2">v2</a>, <a href="https://ncatlab.org/nlab/show/Elements+of+%E2%88%9E-Category+Theory">current</a>

   touched the formatting

   added doi:10.1017/9781108936880

   added pdf

   added what it’s about:

   on (∞,1)-category theory formulated via ∞-cosmoi and the homotopy 2-category of (∞,1)-categories (formal $(\infty,1)$-category theory).

   added pointer to related texts:

   • Emily Riehl, Dominic Verity, The 2-category theory of quasi-categories, Advances in Mathematics 280 (2015) 549-642 $[$arXiv:1306.5144, doi:10.1016/j.aim.2015.04.021$]$

   • Emily Riehl, Dominic Verity, Infinity category theory from scratch, Higher Structures Vol 4, No 1 (2020) $[$arXiv:1608.05314, pdf$]$

   • Emily Riehl, The formal theory of ∞-categories, talk at Categories and Companions Symposium June 8–12, 2021 (video)

   added category:reference-tag

   cross-linked back to this new entry form entries that are referencing this book

   diff, v2, current