All Questions
Tagged with braided-tensor-categories higher-category-theory
7
questions
13
votes
1
answer
589
views
Unobstructedness of braided deformations of symmetric monoidal categories in higher category theory
Let $k$ be a field of characteristic zero, and $\mathcal{C}$ be a $k$-linear additive symmetric monoidal category. A braided deformation of $\mathcal{C}$ over a local artin ring $R$ with residue ...
- 25.1k
8
votes
2
answers
498
views
Why does a tetracategory with one object, one 1-morphism and one 2-morphism give a symmetric monoidal category
According to the periodic table of k-tuply monoidal n-categories, it should be the case that a tetracategory (= weak 4-category) with one object, one 1-morphism and one 2-morphism is effectively ...
- 2,423
6
votes
1
answer
327
views
When is this braiding not a symmetry?
Given a topological space $X$ instead of forming the fundamental groupoid $\pi(X)$ which is the category whose objects are the points and morphisms the homotopy classes of paths one can also form the ...
- 1,614
5
votes
1
answer
220
views
Categorical Morita equivalence implies equivalence of module categories?
Classically, two rings $R$ and $S$ are Morita equivalent if and only if any of the following is true
($R$-Mod) $\simeq$ ($S$-Mod).
$S \simeq Hom_R(M,M)$, where $M$ is a finitely generated projective ...
- 4,760
4
votes
0
answers
99
views
Tensor algebras in the bicategory $\mathsf{2Vect}$
To my knowledge there are two main approaches to categorify the notion of a vector space. I will refer to them as BC-2-vector spaces (Baez, Crans) and KV-2-vector spaces (Kapranov, Voevodsky). Both ...
- 1,527
1
vote
1
answer
118
views
Braided R-matrices for finite action groupoids
1. Algebra from action groupoids
Let $G$ be a finite group acting on a finite set $X$ from the
right (denoted in element as $x^{g}$). We have an algebra (of the
action groupoid) over $\mathbb{C}$: the ...
- 4,760
1
vote
0
answers
87
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 $2$-...
- 1,527