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)...
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| Published in | Theory and applications of categories Vol. 44; no. 26; p. 783 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Sackville
R. Rosebrugh
01.01.2025
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1201-561X |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Lee, Seunghun |
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| SubjectTerms | Algebra Categories Equivalence Localization Theoretical mathematics |
| Title | Equivalences of categories and a model structure on relative categories |
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