Exponentiable Grothendieck categories in flat Algebraic Geometry
| Autor: | Di Liberti, Ivan, González, Julia Ramos |
|---|---|
| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.jalgebra.2022.03.040 |
| Popis: | We introduce and describe the $2$-category $\mathsf{Grt}_{\flat}$ of Grothendieck categories and flat morphisms between them. First, we show that the tensor product of locally presentable linear categories $\boxtimes$ restricts nicely to $\mathsf{Grt}_{\flat}$. Then, we characterize exponentiable objects with respect to $\boxtimes$: these are 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 $\mathsf{Qcoh}(X)$ is exponentiable. Finally, we provide a family of examples and concrete computations of exponentials. Comment: Final version. Accepted for publication |
| Databáze: | arXiv |
| Externí odkaz: |
|