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- W4384644626 abstract "In this paper we show that if $mathscr{C}$ is a tangent category then the Ind-category $operatorname{Ind}(mathscr{C})$ is a tangent category as well with a tangent structure which locally looks like the tangent structure on $mathscr{C}$. Afterwards we give a pseudolimit description of $operatorname{Ind}(mathscr{C})_{/X}$ when $mathscr{C}$ admits finite products, show that the $operatorname{Ind}$-tangent category of a representable tangent category remains representable (in the sense that it has a microlinear object), and we characterize the differential bundles in $operatorname{Ind}(mathscr{C})$ when $mathscr{C}$ is a Cartesian differential category. Finally we compute the $operatorname{Ind}$-tangent category for the categories $mathbf{CAlg}_{A}$ of commutative $A$-algebras, $mathbf{Sch}_{/S}$ of schemes over a base scheme $S$, $A$-$mathbf{Poly}$ (the Cartesian differential category of $A$-valued polynomials), and $mathbb{R}$-$mathbf{Smooth}$ (the Cartesian differential category of Euclidean spaces). In particular, during the computation of $operatorname{Ind}(mathbf{Sch}_{/S})$ we give a definition of what it means to have a formal tangent scheme over a base scheme $S$." @default.
- W4384644626 created "2023-07-19" @default.
- W4384644626 creator A5082149909 @default.
- W4384644626 date "2023-07-16" @default.
- W4384644626 modified "2023-10-18" @default.
- W4384644626 title "Tangent Ind-Categories" @default.
- W4384644626 doi "https://doi.org/10.48550/arxiv.2307.08183" @default.
- W4384644626 hasPublicationYear "2023" @default.
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