21 citations · 79 across the 11 of their papers we have counts for
11 papers
Extension Theory and Fermionic Strongly Fusion 2-Categories (with an Appendix by Thibault Didier Décoppet and Theo Johnson-Freyd)
Thibault Didier Décoppet
We study group graded extensions of fusion 2-categories. As an application, we obtain a homotopy theoretic classification of fermionic strongly fusion 2-categories. We examine vari…
On the Dualizability of Fusion 2-Categories
Thibault D. Décoppet
Over an arbitrary field, we prove that the relative 2-Deligne tensor product of two separable module 2-categories over a compact semisimple tensor 2-category exists. This allows us…
Local Modules in Braided Monoidal 2-Categories
Thibault D. Décoppet, Hao Xu
Given an algebra in a monoidal 2-category, one can construct a 2-category of right modules. Given a braided algebra in a braided monoidal 2-category, it is possible to refine the n…
Fiber 2-Functors and Tambara-Yamagami Fusion 2-Categories
Thibault D. Décoppet, Matthew Yu
We introduce group-theoretical fusion 2-categories, a strong categorification of the notion of a group-theoretical fusion 1-category. Physically speaking, such fusion 2-categories…
Drinfeld Centers and Morita Equivalence Classes of Fusion 2-Categories
Thibault D. Décoppet
We prove that the Drinfeld center of a fusion 2-category is invariant under Morita equivalence. We go on to show that the concept of Morita equivalence between connected fusion 2-c…
The Morita Theory of Fusion 2-Categories
Thibault D. Décoppet
We develop the Morita theory of fusion 2-categories. In order to do so, we begin by proving that the relative tensor product of modules over a separable algebra in a fusion 2-categ…
Rigid and Separable Algebras in Fusion 2-Categories
Thibault D. Décoppet
Rigid monoidal 1-categories are ubiquitous throughout quantum algebra and low-dimensional topology. We study a generalization of this notion, namely rigid algebras in an arbitrary…
The Relative Deligne Tensor Product over Pointed Braided Fusion Categories
Thibault D. Décoppet
We give a formula for the relative Deligne tensor product of two indecomposable finite semisimple module categories over a pointed braided fusion category over an algebraically clo…
Compact Semisimple 2-Categories
Thibault D. Décoppet
Working over an arbitrary field, we define compact semisimple 2-categories, and show that every compact semisimple 2-category is equivalent to the 2-category of separable module 1-…
Finite Semisimple Module 2-Categories
Thibault D. Décoppet
Let be a multifusion 2-category. We show that every finite semisimple -module 2-category is canonically enriched over . Using this enrich…
Weak Fusion 2-Categories
Thibault D. Décoppet
We introduce a weakening of the notion of fusion 2-category given in arXiv:1812.11933. Then, we establish a number of properties of (multi)fusion 2-categories. Finally, we describe…