Abstract:We define perfect morphisms to be those which are the pullback of their image under a given endofunctor. The interplay of these morphisms with other generalisations of perfect maps is investigated. In particular, closure operator theory is used to link closure and orthogonality properties of such morphisms. A number of detailed examples are given.
Keywords: perfect morphism, (pullback) closure operator, factorisation theory, orthogonal morphisms
AMS Subject Classification: 18A20, 18B30, 54C10