Grothendieck Categories and Support Conditions

Grothendieck Categories and Support Conditions

Grothendieck Categories and Support Conditions

Injectivity in a category: an overview on smallness conditions

Some of the so called smallness conditions in algebra as well as in category theory, are important and interesting for their own and also tightly related to injectivity, are essential boundedness, cogenerating set, and residual smallness. In this overview paper, we first try to refresh these smallness condition by giving the detailed proofs of the results mainly by Bernhard Banaschewski and W...

The Grothendieck Construction and Gradings for Enriched Categories

The Grothendieck construction is a process to form a single category from a diagram of small categories. In this paper, we extend the definition of the Grothendieck construction to diagrams of small categories enriched over a symmetric monoidal category satisfying certain conditions. Symmetric monoidal categories satisfying the conditions in this paper include the category of k-modules over a c...

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