We show that lax epimorphisms in the category Cat are precisely the functors P : E −→ B for which the functor P * : [B, Set] −→ [E, Set] of composition with P is fully faithful. We present two other characterizations. Firstly, lax epimorphisms are precisely the " absolutely dense " functors, i.e., functors P such that every object B of B is an absolute… (More)
We show that the category of regular epimorphisms in a Barr exact Goursat category is almost Barr exact in the sense that (it is a regular category and) every regular epimorphism in it is an effective descent morphism.
The categorical definition of semidirect products was introduced by D. Bourn and G. Janelidze in , where they proved that, in the category of groups, this notion coincides with the classical one. A characterization of pointed categories with categorical semidirect products was given in . The existence of such products imply, in particular, that the… (More)
A characterization of descent morphism in the category of Priestley spaces, as well as necessary and sufficient conditions for such morphisms to be effective are given. For that we embed this category in suitable categories of preordered topological spaces were descent and effective morphisms are described using the monadic description of descent. A… (More)
We characterize the (effective) E-descent morphisms in the category Cat of small categories, when E is the class of discrete fibrations or the one of discrete cofibrations, and prove that every effective global-descent morphism is an effective E-descent morphism while its converse fails.