semimodel category

Introduced by Hovey in 1998, semimodel categories are a relaxation of model categories that allows for a largely similar theory.

The notion of a weak model category and premodel category relaxes the definition even further.

(See Hovey, Theorem 3.3.)

A **left semimodel category** is a relative category equipped with a class of cofibrations and fibrations such that weak equivalences are closed under retracts and the 2-out-of-3 property, cofibrations have a left lifting property with respect to trivial fibrations, trivial cofibrations with cofibrant source have a left lifting property with respect to fibrations, and morphisms with cofibrant source can be factored as a cofibration followed by a fibration, either one of which can be further made trivial.

A **right semimodel category** is defined by passing to the opposite category.

- Mark Hovey,
*Monoidal model categories*, arXiv:math/9803002.

Last revised on May 7, 2020 at 20:54:15. See the history of this page for a list of all contributions to it.