Estudo Geralhttps://estudogeral.sib.uc.ptThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Mon, 23 Sep 2019 20:30:30 GMT2019-09-23T20:30:30Z5011On functors which are lax epimorphismshttp://hdl.handle.net/10316/11460Title: On functors which are lax epimorphisms
Authors: Adámek, Jirí; Bashir, Robert El; Sobral, Manuela; Velebil, Jirí
Abstract: We show that lax epimorphisms in the category Cat are precisely the functors P : Ε → 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 colimit of all arrows P(E) → B for E in E. Secondly, lax epimorphisms are precisely the functors P such that for every morphism f of B the category of all factorizations through objects of P[E] is connected.
A relationship between pseudoepimorphisms and lax epimorphisms is discussed.
Mon, 01 Jan 2001 00:00:00 GMThttp://hdl.handle.net/10316/114602001-01-01T00:00:00Z