On lax epimorphisms and the associated factorization

Abstract

We study lax epimorphisms in 2-categories, with special attention to $\mathsf{Cat}$ and $\mathcal{V}$-$\mathsf{Cat}$. 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 $\mathsf{Cat}$.

References in corpus (1)

• Categorical structures enriched in a quantaloid: categories, distributors and functors

Cited by in corpus (2)

• Cauchy Completeness, Lax Epimorphisms and Effective Descent for Split Fibrations
• Comparing semantic frameworks for dependently-sorted algebraic theories