On lax epimorphisms and the associated factorization

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On lax epimorphisms and the associated factorization
 
Lucatelli Nunes, Fernando; Sousa, Lurdes
(2022) Journal of Pure and Applied Algebra, volume 226, issue 12, pp. 1 - 27
(Article)
Abstract
We study lax epimorphisms in 2-categories, with special attention to Cat and V-Cat. We show that any 2-category with convenient colimits has an orthogonal LaxEpi-factorization system, and we give a concrete description of this factorization in Cat.
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Keywords: 2-categories, Enriched categories, Factorization systems, Fully faithful morphisms, Weighted (co)limits, Taverne, Algebra and Number Theory
DOI: https://doi.org/10.1016/j.jpaa.2022.107126
ISSN: 0022-4049
Publisher: Elsevier
Note: Funding Information: This research was partially supported by the Centre for Mathematics of the University of Coimbra - UIDB/00324/2020 , funded by the Portuguese Government through FCT/MCTES . Publisher Copyright: © 2022 Elsevier B.V.
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