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I have heard that one can do algebraic geometry internal to symmetric monoidal categories. Topological quantum field theories also exist internal to symmetric monoidal categories, and the usual defini …

Given a category $\mathcal{C}$, we can define the category of endofunctors $\operatorname{Cat}(\mathcal{C})$, with objects functors $F: \mathcal{C} \to \mathcal{C}$ and morphisms natural transformatio …

Chris Schommer-Pries has classified 2d extended TQFTs (topological quantum field theories) in his PhD thesis. The result is a (not necessarily abelian) separable symmetric Frobenius algebra (possibly …

In a sense, this is a follow up on this question, but one PhD programme later. Let $\mathcal{C}$ be ribbon fusion. By $\mathcal{C}'$, we denote the symmetric centre, i.e. the full subcategory of obje …

In general, one extracts a manifold invariant from a TQFT by interpreting the closed manifold as a bordism from the empty set to the empty set. The TQFT sends this bordism to a homomorphism of the gro …

In Walker and Wang's article about (3+1)-TQFTs from premodular categories, they say on page 14 that you can take a quotient of a premodular category $\mathcal{C}$ by its symmetric fusion subcategory …