Exponentiable Grothendieck categories in flat algebraic geometry

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F22%3A00557712" target="_blank" >RIV/67985840:_____/22:00557712 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.jalgebra.2022.03.040" target="_blank" >https://doi.org/10.1016/j.jalgebra.2022.03.040</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jalgebra.2022.03.040" target="_blank" >10.1016/j.jalgebra.2022.03.040</a>

Result language
angličtina
Original language name
Exponentiable Grothendieck categories in flat algebraic geometry
Original language description
We introduce and describe the 2-category Grt♭ of Grothendieck categories and flat morphisms between them. First, we show that the tensor product of locally presentable linear categories ⊠ restricts nicely to Grt♭. 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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GX20-31529X" target="_blank" >GX20-31529X: Abstract convergence schemes and their complexities</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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