On lax epimorphisms and the associated factorization

• DOI: 10.48550/arxiv.2109.09836
• Publication Date: 2021-01-01
• Authors: Fernando Lucatell...; Lurdes Sousa
• Keywords: Algebra and Number Theory; Fully faithful morphisms; Mathematics - Category Theory; 0102 computer and information sciences; 18N10, 18A20, 18D20, 18A32, 18A22; 01 natural sciences; Factorization systems; Enriched categories; Weighted (co)limits; Taverne; FOS: Mathematics; Category Theory (math.CT); 0101 mathematics; 2-categories

We study lax epimorphisms in 2-categories, with special attention to $\mathsf{Cat}$ and $\mathcal{V}$-$\mathsf{Cat}$. show that any 2-category convenient colimits has an orthogonal $LaxEpi$-factorization system, we give a concrete description of this factorization $\mathsf{Cat}$.