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.
Keywords: Equivalence of category, Model category, Relative category
2020 MSC: 18N40
Theory and Applications of Categories, Vol. 44, 2025, No. 26, pp 783-804.
Published 2025-08-28.
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