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
equivalences in/of $(\infty,1)$-categories
This entry is about the book
William Dwyer, Philip Hirschhorn, Daniel Kan, Jeff Smith,
Homotopy Limit Functors on Model Categories and Homotopical Categories
volume 113 of Mathematical Surveys and Monographs.
(pdf)
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.
Compare also