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 Abenriched 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 alphapresentable 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 alphacocomplete tensor product. This allows us to translate the functoriality, simmetry and commutativity of Kelly's tensor product to the tensor product of Grothendieck categories.
