model category, model -category
Definitions
Morphisms
Universal constructions
Refinements
Producing new model structures
Presentation of -categories
Model structures
for -groupoids
on chain complexes/model structure on cosimplicial abelian groups
related by the Dold-Kan correspondence
for equivariant -groupoids
for rational -groupoids
for rational equivariant -groupoids
for -groupoids
for -groups
for -algebras
general -algebras
specific -algebras
for stable/spectrum objects
for -categories
for stable -categories
for -operads
for -categories
for -sheaves / -stacks
Introduced by Hovey 1998, the notion of semimodel categories s a relaxation of that of model categories which allows for a largely similar theory.
The notion of a weak model category and premodel category relaxes the definition even further.
(See Hovey 98, 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.
(semimodel structure on semisimplicial sets) There exists a right semi-model structure on the category of semi-simplicial sets (Rooduijn 2018).
The definition is due to:
The example of the semimodel structure on semisimplicial sets:
Last revised on June 26, 2021 at 12:00:52. See the history of this page for a list of all contributions to it.