nLab Homotopy Limit Functors on Model Categories and Homotopical Categories



Homotopy theory

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



Paths and cylinders

Homotopy groups

Basic facts


(,1)(\infty,1)-Category theory

This entry is about the book

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:

category: reference

Last revised on June 24, 2022 at 10:12:23. See the history of this page for a list of all contributions to it.