Equivalences of categories and a model structure on relative categories

We show that there is a model structure on the category RelCat of small relative categories such that for a morphism f in RelCat, f is a weak equivalence iff the associated functor on homotopy 1-categories is an equivalence of categories. In this model category (i) every object is cofibrant and (ii)...

Full description

Saved in:
Bibliographic Details
Published inTheory and applications of categories Vol. 44; no. 26; p. 783
Main Author Lee, Seunghun
Format Journal Article
LanguageEnglish
Published Sackville R. Rosebrugh 01.01.2025
Subjects
Algebra
Categories
Equivalence
Localization
Theoretical mathematics
Online AccessGet full text
ISSN1201-561X

Cover

More Information
Summary:We show that there is a model structure on the category RelCat of small relative categories such that for a morphism f in RelCat, f is a weak equivalence iff the associated functor on homotopy 1-categories is an equivalence of categories. In this model category (i) every object is cofibrant and (ii) the homotopy category functor becomes a fibrant replacement. The model structure is left-induced from the model category on small categories with equivalences of categories as weak equivalences by the homotopy category functor in a Quillen equivalent way.
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:1201-561X