Zobrazeno 1 - 10
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pro vyhledávání: '"Thibault, D."'
Autor:
Décoppet, Thibault D.
Over a field of characteristic $p>0$, the higher Verlinde categories $\mathrm{Ver}_{p^n}$ are obtained by taking the abelian envelope of quotients of the category of tilting modules for the algebraic group $\mathrm{SL}_2$. These symmetric tensor cate
Externí odkaz:
http://arxiv.org/abs/2407.20211
Autor:
Décoppet, Thibault D.
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 to consider the Morita 4-category of compact semisimple tensor 2-cate
Externí odkaz:
http://arxiv.org/abs/2311.16827
Autor:
Décoppet, Thibault D., Xu, Hao
Publikováno v:
J. Math. Phys. 65, 061702 (2024)
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 notion of right module to that of a local module. Under mild assumption
Externí odkaz:
http://arxiv.org/abs/2307.02843
Autor:
Décoppet, Thibault D., Yu, Matthew
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 arise by gauging subgroups of a global symmetry. We show that group-th
Externí odkaz:
http://arxiv.org/abs/2306.08117
Autor:
Décoppet, Thibault D., Yu, Matthew
Publikováno v:
Lett. Math. Phys. 113, 36 (2023)
We generalize the notion of an anomaly for a symmetry to a noninvertible symmetry enacted by surface operators using the framework of condensation in 2-categories. Given a multifusion 2-category, potentially with some additional levels of monoidality
Externí odkaz:
http://arxiv.org/abs/2211.08436
Autor:
Décoppet, Thibault D.
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-categories recovers exactly the notion of Witt equivalence between brai
Externí odkaz:
http://arxiv.org/abs/2211.04917
Autor:
Décoppet, Thibault D.
Publikováno v:
Higher Structures 7(1):234-292, 2023
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-category exists. We use this result to construct the Morita 3-category of s
Externí odkaz:
http://arxiv.org/abs/2208.08722
Autor:
Décoppet, Thibault D.
Publikováno v:
Advances in Mathematics 419 (2023) 108967
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 monoidal 2-category. Examples of rigid algebras include $G$-graded fus
Externí odkaz:
http://arxiv.org/abs/2205.06453
Autor:
Décoppet, Thibault D.
Publikováno v:
J. Algebra 620 (2023) 89-112
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 closed field.
Comment: Minor corrections
Comment: Minor corrections
Externí odkaz:
http://arxiv.org/abs/2203.10331
Autor:
Décoppet, Thibault D.
Publikováno v:
Trans. Amer. Math. Soc., 376(12):8309-8336, 2023
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-categories over a finite semisimple tensor 1-category. Then, we prove
Externí odkaz:
http://arxiv.org/abs/2111.09080