Centre for Mathematics, University of Coimbra

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Type:	Preprint
National /International:	International
Title:	Semantic factorization and descent
Publication Date:	2019-02-01
Authors:	- Fernando Lucatelli Nunes
Abstract:	Let A be a 2-category with suitable opcomma objects and pushouts. We give a direct proof that, provided that the codensity monad of a morphism p exists and is preserved by a suitable morphism, the factorization given by the lax descent object of the higher cokernel of p is up to isomorphism the same as the semantic factorization of p, either one existing if the other does. The result can be seen as a counterpart account to the celebrated Bénabou-Roubaud theorem. This leads in particular to a monadicity theorem, since it characterizes monadicity via descent. It should be noted that all the conditions on the codensity monad of p trivially hold whenever p has a left adjoint and, hence, in this case, we find monadicity to be a 2-dimensional exact condition on p, namely, to be a 2-effective monomorphism of the 2-category A.
Institution:	DMUC 19-03
Online version:	http://www.mat.uc.pt...prints/eng_2019.html
Download:	Not available