# nLab Homotopy Limit Functors on Model Categories and Homotopical Categories

References

### Context

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

(∞,1)-category theory

## Models

This entry is about the book

• Homotopy Limit Functors on Model Categories and Homotopical Categories

Mathematical Surveys and Monographs 113

AMS 2004

ISBN: 978-1-4704-1340-8

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.

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.

## References

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.