INTERNAL MONOTONE-LIGHT FACTORIZATION FOR CATEGORIES VIA PREORDERS Dedicated to Aurelio Carboni on the occasion of his sixtieth birthday
نویسنده
چکیده
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.
منابع مشابه
SEMI - ABELIAN MONADIC CATEGORIES Dedicated to Aurelio Carboni on the occasion of his sixtieth birthday . MARINO GRAN AND
We characterize semi-abelian monadic categories and their localizations. These results are then used to obtain a characterization of pointed protomodular quasimonadic categories, and in particular of protomodular quasivarieties.
متن کاملCOMMUTATOR THEORY IN STRONGLY PROTOMODULAR CATEGORIES Dedicated to Aurelio Carboni on the occasion of his sixtieth birthday
We show that strongly protomodular categories (as the category Gp of groups for instance) provide an appropriate framework in which the commutator of two equivalence relations do coincide with the commutator of their associated normal subobjects, whereas it is not the case in any semi-abelian category.
متن کاملGENERIC MORPHISMS, PARAMETRIC REPRESENTATIONS AND WEAKLY CARTESIAN MONADS Dedicated to Aurelio Carboni on the occasion of his sixtieth birthday
Two notions, generic morphisms and parametric representations, useful for the analysis of endofunctors arising in enumerative combinatorics, higher dimensional category theory, and logic, are defined and examined. Applications to the Batanin approach to higher category theory, Joyal species and operads are provided.
متن کاملON EXTENSIONS OF LAX MONADS Dedicated to Aurelio Carboni on the occasion of his sixtieth birthday
In this paper we construct extensions of Set-monads – and, more generally, of lax Rel-monads – into lax monads of the bicategory Mat(V) of generalized V-matrices, whenever V is a well-behaved lattice equipped with a tensor product. We add some guiding examples.
متن کاملA Galois Theory with Stable Units for Simplicial Sets
We recall and reformulate certain known constructions, in order to make a convenient setting for obtaining generalized monotone-light factorizations in the sense of A. Carboni, G. Janelidze, G. M. Kelly and R. Paré. This setting is used to study the existence of monotone-light factorizations both in categories of simplicial objects and in categories of internal categories. It is shown that ther...
متن کامل