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2
votes
0
answers
128
views
Generalization of monoidal category with tensor products of $n$ objects
I'm looking for a generalization of monoidal categories, say $n$-monoidal categories, s.t. an ordinary monoidal category is the $n=2$ case. For general $n$, naively it should consist (among other data …
4
votes
1
answer
358
views
Does the functor $\mathcal{C} \to \mathcal{Z}(\mathcal{C})$ have adjoints?
Let $\mathcal{C}$ be a braided monoidal category. We have a canonical functor $\mathcal{C} \to \mathcal{Z}(\mathcal{C})$ from $\mathcal{C}$ to the Drinfeld center $\mathcal{Z}(\mathcal{C})$ sending an …
4
votes
0
answers
145
views
Hopf monoid from comonoidal structures
Let $\mathcal{V}$ be a closed braided monoidal category and $\mathcal{V}-Cat$ the monoidal bicategory of small $\mathcal{V}$-enriched categories. Let $\mathcal{C}$ be a pseudo-comonoid in $\mathcal{V} …
8
votes
0
answers
207
views
Categorical interpretation of quantum double $D(A,B,\eta)$
It is known that the Drinfel'd double $D(A)$ of a Hopf algebra $A$ is characterized by the following two properties:
The category of left $D(A)$-modules $_{D(A)}\mathcal{M}$ is equivalent to the ca …
4
votes
0
answers
66
views
Categorical construction of comodule category of FRT algebra
Let $\mathcal{B}$ denote the braid groupoid, with objects being non-negative integers $n \in \mathbb{Z}_{\geq 0}$ and morphisms $\mathcal{B}(n,n)=B_{n}$ given by the braid group. Let $\mathcal{C}$ be …
1
vote
0
answers
82
views
Braided category inside braided 2-category
Let $\mathcal{C}$ be a semistrict braided monoidal $2$-category in the sense of [BN] (so in particular a strict $2$-category). Let $\mathcal{C}_1$ be the category of $1$-morphisms (objects) and $2$-mo …