Higher Dualizability and Singly-Generated Grothendieck Categories
نویسندگان
چکیده
Let k be a field. We show that locally presentable, k-linear categories $${\mathcal {C}}$$ dualizable in the sense identity functor can recovered as $$\coprod _i x_i\otimes f_i$$ for objects $$x_i\in {\mathcal and left adjoints $$f_i$$ from to $$\mathrm {Vect}_k$$ are products of copies . This partially confirms conjecture by Brandenburg, author T. Johnson-Freyd. Motivated this, we also characterize Grothendieck containing an object x with property every is copower x: they precisely non-singular injective right modules over simple, regular, self-injective rings type I or III.
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ژورنال
عنوان ژورنال: Applied Categorical Structures
سال: 2021
ISSN: ['1572-9095', '0927-2852']
DOI: https://doi.org/10.1007/s10485-021-09645-x