# nLab Model Categories and More General Abstract Homotopy Theory

A historically important early manuscript draft:

• Model Categories and More General Abstract Homotopy Theory

(1997)

on model category-theory in general and on cofibrantly generated model categories and Reedy model categories in particular.

This manuscript draft later transformed in Homotopy Limit Functors on Model Categories and Homotopical Categories, adding Jeffrey H. Smith as a coauthor.

However, 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).

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.

The first mention of monoidal model categories (without the unit axiom) under this name is in Remark 55.10, with no definition given, but the preceding section discusses the pushout product axiom.

All this material did not make it to the book.

category: reference

Last revised on August 9, 2022 at 15:57:12. See the history of this page for a list of all contributions to it.