Di Liberti, Ivan
Ramos González, Julia
[UCL]
We introduce and describe the 2-category of Grothendieck categories and flat morphisms between them. First, we show that the tensor product of locally presentable linear categories ⊠ restricts nicely to Gr_flat. Then, we characterize exponentiable objects with respect to ⊠: these are the continuous Grothendieck categories. In particular, locally finitely presentable Grothendieck categories are exponentiable. Consequently, we have that, for a quasi-compact quasi-separated scheme X, the category of quasi-coherent sheaves QCoh(X) is exponentiable. Finally, we provide a family of examples and concrete computations of exponentials.
Bibliographic reference |
Di Liberti, Ivan ; Ramos González, Julia. Exponentiable Grothendieck categories in flat algebraic geometry. In: Journal of Algebra, Vol. 604, no.-, p. 362-405 (2022) |
Permanent URL |
http://hdl.handle.net/2078.1/260492 |