Minimal resolutions and other minimal models

Abstract

In many situations, minimal models are used as representatives of homotopy types. In this paper we state this fact as an equivalence of categories . This equivalence follows from an axiomatic definition of minimal objects. We see that this definition includes examples such as minimal resolutions of Eilenberg-Nakayama-Tate, minimal fiber spaces of Kan and A-minimal A-extensions of Halperin . For the first one, this is done by generalizing the construction of minimal resolutions of modules to complexes. The others follow by a caracterization of minimal objects in bifibred categories.