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 Internal monotone-light factorization for categories via preorders
Please use this identifier to cite or link to this item http://hdl.handle.net/10773/8451

title: Internal monotone-light factorization for categories via preorders
authors: Xarez, J.J.
keywords: (reflexive) graph
(reflexive) relation
Category
Preorder
Factorization system
Localization
Stabilization
Descent theory
Galois theory
Monotone-light factorization
issue date: 2004
publisher: Mount Allison University
abstract: It is shown that, for a finitely-complete category C with coequalizers of kernel pairs, if every product-regular epi is also stably-regular then there exist the reflections (R)Grphs(C) → (R)Rel(C), from (reflexive) graphs into (reflexive) relations in C, and Cat(C) → Preord(C), from categories into preorders in C. Furthermore, such a sufficient condition ensures as well that these reflections do have stable units. This last property is equivalent to the existence of a monotone-light factorization system, provided there are sufficiently many effective descent morphisms with domain in the respective full subcategory. In this way, we have internalized the monotone-light factorization for small categories via preordered sets, associated with the reflection Cat → Preord, which is now just the special case C = Set.
URI: http://hdl.handle.net/10773/8451
ISSN: 1201-561X
publisher version/DOI: http://www.tac.mta.ca/tac/
source: Theory and Applications of Categories
appears in collectionsCIDMA - Artigos

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