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- W3158601142 abstract "Let k be a field. We show that locally presentable, k-linear categories $${mathcal {C}}$$ dualizable in the sense that the identity functor can be recovered as $$coprod _i x_iotimes f_i$$ for objects $$x_iin {mathcal {C}}$$ and left adjoints $$f_i$$ from $${mathcal {C}}$$ to $$mathrm {Vect}_k$$ are products of copies of $$mathrm {Vect}_k$$ . This partially confirms a conjecture by Brandenburg, the author and T. Johnson-Freyd. Motivated by this, we also characterize the Grothendieck categories containing an object x with the property that every object is a copower of x: they are precisely the categories of non-singular injective right modules over simple, regular, right self-injective rings of type I or III." @default.
- W3158601142 created "2021-05-10" @default.
- W3158601142 creator A5076253324 @default.
- W3158601142 date "2021-04-22" @default.
- W3158601142 modified "2023-09-23" @default.
- W3158601142 title "Higher Dualizability and Singly-Generated Grothendieck Categories" @default.
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- W3158601142 doi "https://doi.org/10.1007/s10485-021-09645-x" @default.
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