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Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.

4 votes
0 answers
161 views

Drinfeld center of a tensor category

Firstly, apologies for the imprecise language, I'm a physicist trying to understand anyonic excitations from the lens of category theory. If I have a category (say $\operatorname{Rep}(\mathbb{Z}_2)$) …
pyroscepter's user avatar
3 votes
0 answers
139 views

Understanding fusion categories from the perspective of anyons?

ncatlab defines a fusion category as "A fusion category is a rigid semisimple linear (Vect-enriched) monoidal category (“tensor category”), with only finitely many isomorphism classes of simple object …
pyroscepter's user avatar
3 votes
2 answers
108 views

Does unitarity and modularity constrain fusion multiplicities to be 0,1?

If I have a braided tensor category that's unitary and modular, then how does the unitarity and modularity constrain the fusion multiplicities? I know that if $a,b,c \in ob({C})$ satisfy the fusion ru …
pyroscepter's user avatar