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  • Jiř´i Ad´amek, Robert El Bashir, Manuela Sobral, Jiř´i Velebil
  • 2001
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)
The categorical definition of semidirect products was introduced by D. Bourn and G. Janelidze in [2], 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 [3]. The existence of such products imply, in particular, that the(More)
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