Exponentiable Grothendieck categories in flat algebraic geometry
(2023) Journal of Algebra — Vol. 604, p. 362-405 (2022)
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- Authors
Ramos González, Julia 
- Abstract
- 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.
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Citations
Di Liberti, I., & Ramos González, J. (2023). Exponentiable Grothendieck categories in flat algebraic geometry. Journal of Algebra, 604, 362-405. https://doi.org/10.1016/j.jalgebra.2022.03.040 (Original work published 2022)