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From nonabelian basechange to basechange with coefficients
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abstract
The goal of this paper is to explain when basechange theorems for sheaves of spaces imply basechange for sheaves with coefficients in other presentable $\infty$-categories. We accomplish this by analyzing when the tensor product of presentable $\infty$-categories preserves left adjointable squares. As a sample result, we show that the Proper Basechange Theorem in topology holds with coefficients in any presentable $\infty$-category which is compactly generated or stable. We also prove results about the interaction between tensor products of presentable $\infty$-categories and various categorical constructions that are of independent interest.
Forward citations
Cited by 2 Pith papers
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Enriched $\infty$-categories as marked module categories
Enriched ∞-categories are equivalent to presentable module categories marked by an atomically generating family of representables.
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On the Bauer--Furuta construction
Using six-functor sheaf theory, the Bauer-Furuta invariant is defined as the proper pushforward f_* f^!(1), with f^!(1) computed as the Thom spectrum of the family index.
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