2017/11/28 by Alan S. Cigoli, Cigoli, Alan S., Tomas Everaert +3
Mathematics · Medicine · #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Intracranial Aneurysms: Treatment and Complications #math.AT #math.CT
paper · pdf · doi:10.48550/arxiv.1711.10450
final version accepted for publication
openalex publication_date 2017/11/28 · arxiv created 2018/01/02 · arxiv updated 2018/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given an exact category C, it is well known that the connected component reflector π0\colonGpd(C)\toC from the category Gpd(C) of internal groupoids in C to the base category C is semi-left-exact. In this article we investigate the existence of a monotone-light factorisation system associated with this reflector. We show that, in general, there is no monotone-light factorisation system (E',M^*) in Gpd(C), where M^* is the class of coverings in the sense of the corresponding Galois theory. However, when restricting to the case where C is an exact Mal'tsev category, we show that the so-called comprehensive factorization of regular epimorphisms in Gpd(C) is the relative monotone-light factorisation system (in the sense of Chikhladze) in the category Gpd(C) corresponding to the connected component reflector, where E' is the class of final functors and M^* the class of regular epimorphic discrete fibrations.