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- W3131404845 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.
- W3131404845 created "2021-03-01" @default.
- W3131404845 creator A5076253324 @default.
- W3131404845 date "2021-02-14" @default.
- W3131404845 modified "2023-09-27" @default.
- W3131404845 title "Higher dualizability and singly-generated Grothendieck categories" @default.
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