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    • CommentRowNumber1.
    • CommentAuthorDmitri Pavlov
    • CommentTimeMay 7th 2022


    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





    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


    Glossary of Notation


    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMay 8th 2022
    • (edited May 8th 2022)

    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 (,1)(\infty,1)-category theory).

    added pointer to related texts:

    added category:reference-tag

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

    diff, v2, current