categories: connected functors and pseudoepis

[Jiri Adamek <adamek@iti.cs.tu-bs.de>]

The connected functors we have mentioned the other day, i.e. those
functors  p: E -> B  for which  (-).p Set^B -> Set^E  is fully faithful,
are easily seen to be precisely the lax epimorphisms of the 2-category Cat
(of small categories). We do not know whether every pseudoepimorphism
in Cat is connected, does anyone know? The answer is affirmative if
B  is a preorder.
J.Adamek, R. El Bashir, M. Sobral and J. Velebil



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