Monoidal category theory serves as a powerful framework for describing logical aspects of
quantum theory, giving an abstract language for parallel and sequential composition, and a …

A bstract We classify all non-invertible Kramers-Wannier duality defects in the E 8 lattice
Vertex Operator Algebra (ie the chiral (E 8) 1 WZW model) coming from ℤ m symmetries. We …

We present a higher-categorical generalization of the" Karoubi envelope" construction from
ordinary category theory, and prove that, like the ordinary Karoubi envelope, our higher …

arXiv:1812.11933v1 [math.QA] 31 Dec 2018 Page 1 FUSION 2-CATEGORIES AND A
STATE-SUM INVARIANT FOR 4-MANIFOLDS CHRISTOPHER L. DOUGLAS AND DAVID J …

We prove that every slightly degenerate braided fusion category admits a minimal
nondegenerate extension, and hence that every pseudo-unitary super modular tensor …

We prove a theorem in 3-dimensional topological field theory: a Reshetikhin–Turaev theory
admits a nonzero boundary theory iff it is a Turaev–Viro theory. The proof immediately …

We use modified traces to renormalize Lyubashenko's closed 3-manifold invariants coming
from twist non-degenerate finite unimodular ribbon categories. Our construction produces …

We introduce the normal produoidal category of monoidal contexts over an arbitrary
monoidal category. In the same sense that a monoidal morphism represents a process, a …

We study the question of dualizability in higher Morita categories of locally presentable
tensor categories and braided tensor categories. Our main results are that the 3-category of …

We prove that a finite braided tensor category 𝒜 is invertible in the Morita 4–category BrTens
of braided tensor categories if and only if it is nondegenerate. This includes the case of …