homotopy theory, (∞,1)-category theory, homotopy type theory
flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed…
models: topological, simplicial, localic, …
see also algebraic topology
Introductions
Definitions
Paths and cylinders
Homotopy groups
Basic facts
Theorems
Background
Basic concepts
equivalences in/of $(\infty,1)$-categories
Universal constructions
Local presentation
Theorems
Extra stuff, structure, properties
Models
This entry is about the book
William Dwyer, Philip Hirschhorn, Daniel Kan, Jeff Smith,
Homotopy Limit Functors on Model Categories and Homotopical Categories
Mathematical Surveys and Monographs 113
AMS 2004
on the theory of homotopical categories and model categories – a presentation of (∞,1)-categories –, their simplicial localization/homotopy categories and derived functors such as homotopy limit functors.
A historically important early manuscript draft of this book is
The draft serves as an original reference for the Kan recognition theorem (in §II.8) and the Kan transfer theorem (in §II.9), as well as cofibrantly generated model categories (in Chapter II). This material did not make it to the book.
Furthermore, this draft originates the modern definition of a model category (in §I.1.2), modifying the original definition of closed model category by Quillen by replacing finite (co)limits with small (co)limits and requiring factorizations to be functorial.
Compare also:
Last revised on June 24, 2022 at 10:12:23. See the history of this page for a list of all contributions to it.