We will continue on Thursday, November 28, in M5 at 1pm by the talk

J. R. Gonzales

Grothendieck categories and their tensor product as filtered colimits

Abstract:
Grothendieck categories are the Ab-enriched Grothendieck topoi. In this talk, we will first show two different ways to obtain a Grothendieck category as a filtered colimit of its representing linear sites: one given by all possible representing linear sites, the other, coarser, given by the representing linear sites induced by the full subcategories of alpha-presentable objects, with varying regular cardinal alpha. Making use of the latter, we show that the tensor product of Grothendieck categories, introduced in previous joint work with Lowen and Shoikhet, is compatible via this construction with Kelly's alpha-cocomplete tensor product. This allows us to translate the functoriality, simmetry and commutativity of Kelly's tensor product to the tensor product of Grothendieck categories.