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Results tagged with monoidal-categories
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user 167503
2
votes
0
answers
116
views
Freeness of the action of the ground monoid in a monoidal category
Let $(\mathcal{C}, \otimes , 1)$ be a monoidal category, and let $\mathrm{End}_{\mathcal{C}} (1)$ be the ground monoid of $\mathcal{C}$ - which is a commutative monoid. If $r_X : X \otimes 1 \to X$ de …
- 601
4
votes
1
answer
304
views
Drinfeld center of $\mathrm{Mod}_R$
Let $R$ be a commutative ring and let $\mathrm{Mod}_R$ be the category of (left) $R$-modules.
Question: Is it true that the categories $\mathcal{Z}(\mathrm{Mod}_R)$ and $\mathrm{Mod}_R$ are equivalen …
- 601
1
vote
0
answers
127
views
Recovering the center of a monoid from the Drinfeld center
The Drinfeld center construction is intended to be a categorification of the center of a monoid. It seems to be folklore (eg this answer or this one) that when the Drinfeld center is taken over a mono …
- 601
6
votes
0
answers
109
views
Equivalence between bialgebras and finite ring categories with fibre functor
$\DeclareMathOperator\Rep{Rep}\DeclareMathOperator\Rec{Rec}\DeclareMathOperator\End{End}\DeclareMathOperator\Mod{Mod}\newcommand\fdMod[1]{#1\text-{\Mod}^\text{fd}}$In the celebrated [EGNO, Thm 5.2.3], …
- 601