Exponentiable Grothendieck categories in flat algebraic geometry
نویسندگان
چکیده
We introduce and describe the 2-category Grt♭ of Grothendieck categories flat morphisms between them. First, we show that tensor product locally presentable linear ⊠ restricts nicely to Grt♭. Then, characterize exponentiable objects with respect ⊠: these are continuous categories. In particular, finitely exponentiable. Consequently, have that, for a quasi-compact quasi-separated scheme X, category quasi-coherent sheaves Qcoh(X) is Finally, provide family examples concrete computations exponentials.
منابع مشابه
Exponentiable Functors Between Quantaloid-Enriched Categories
Exponentiable functors between quantaloid-enriched categories are characterized in elementary terms. The proof goes as follows: the elementary conditions on a given functor translate into existence statements for certain adjoints that obey some lax commutativity; this, in turn, is precisely what is needed to prove the existence of partial products with that functor; so that the functor’s expone...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2022
ISSN: ['1090-266X', '0021-8693']
DOI: https://doi.org/10.1016/j.jalgebra.2022.03.040