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https://hdl.handle.net/10316/11460
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. | URI: | https://hdl.handle.net/10316/11460 | Rights: | openAccess |
Appears in Collections: | FCTUC Matemática - Artigos em Revistas Nacionais |
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On functors which are lax epimorphisms.pdf | 244.2 kB | Adobe PDF | View/Open |
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