Colocalization on Grothendieck Categories with Applications to Coalgebras

Atomical Grothendieck Categories

Motivated by the study of Gabriel dimension of a Grothendieck category, we introduce the concept of atomical Grothendieck category, which has only two localizing subcategories, and we give a classification of this type of Grothendieck categories. 1. Introduction. Given a Grothendieck category Ꮽ, we can associate with it the lattice of all localizing categories of Ꮽ and denote it by Tors(Ꮽ). We ...

Towards M-Adhesive Categories based on Coalgebras and Comma Categories

In this contribution we investigate several extensions of the powerset that comprise arbitrarily nested subsets, and call them superpower set. This allows the definition of graphs with possibly infinitely nested nodes. additionally we define edges that are incident to edges. Since we use coalgebraic constructions we refer to these graphs as corecursive graphs. The superpower set functors are ex...

Chain conditions in modular lattices with applications to Grothendieck categories and torsion theories

Distributivity of categories of coalgebras

We prove that for any Set-endofunctor F the category SetF of F -coalgebras is distributive if F preserves preimages, i.e. pullbacks along an injective map, and that the converse is also true whenever SetF has finite products.

Grothendieck Categories and Support Conditions