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Title: On functors which are lax epimorphisms
Authors: Adámek, Jirí 
Bashir, Robert El 
Sobral, Manuela 
Velebil, Jirí 
Keywords: Lax epimorphism
Issue Date: 2001
Publisher: Centro de Matemática da Universidade de Coimbra
Citation: Pré-Publicações DMUC. 01-16 (2001)
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.
Rights: openAccess
Appears in Collections:FCTUC Matemática - Artigos em Revistas Nacionais

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