Multifusion category
Web31 dec. 2024 · Multifusion Categories and Finite Semisimple 2-Categories Thibault D. Décoppet Mathematics 2024 We give a 3-universal property for the Karoubi envelope of a 2-category. Using this, we show that the 3-categories of finite semisimple 2-categories (as introduced in [DR18]) and of multifusion… Expand 6 PDF Save Alert The 2-Deligne … WebA C-linear 2-category Cis finite semisimple if it has finitely many isomorphism classes of simple objects, it is locally finite semisimple, it has adjoints for 1-morphisms, it has direct sums of objects and is 2-idempotent complete. DEFINITION 2.11. A multifusion 2-category is a monoidal finite semisimple 2-category in which all objects ...
Multifusion category
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Web1 aug. 2024 · We show that the canonical 3-functor sending a multifusion categories to its 2-category of finite semisimple module categories induces an equivalence Mult ≃ … Web31 mar. 2024 · Abstract We define the 2-Deligne tensor product of two finite semisimple 2-categories using a 3-universal property, and present its fundamental properties. In particular, we prove that the...
Web17 apr. 2024 · A bicommutant category is a higher categorical analog of a von Neumann algebra. We study the bicommutant categories which arise as the commutant $\mathcal {C}'$ of a fully faithful representation $\mathcal {C}\to\operatorname {Bim} (R)$ of a unitary fusion category $\mathcal {C}$. Web24 ian. 2024 · Given a multifusion 2-category, potentially with some additional levels of monoidality, we prove theorems about the structure of the 2-category obtained by …
Websuperfuse. ( ˌsuːpəˈfjuːz) vb. obsolete to pour or be poured so as to cover something. [C17: from Latin superfūsus poured over, from superfundere, from super- + fundere to pour] WebCondensation inversion and Witt equivalence via generalised orbifolds Vincentas Mulevi cius [email protected] Max-Planck-Institut fur Mathematik, Bonn, Germany In [MR1]
WebFurther, if B is a braided fusion category, the 2-category Mod ( B) inherits a rigid monoidal structure given by the relative Deligne tensor product over B, and so is a fusion 2-category (see [4] for the definition). In particular, the maximal subgroupoid of Mod ( B) is P i c ( B).
Web4 mar. 2024 · Multi-fusion categories are a generalization of fusion categories with a non-simple unit. The direct sum of two multi-fusion categories is again a multi-fusion category. By irreducible I mean that a multi-fusion category cannot be written as a non-trivial direct sum. Are all such irreducible multi-fusion categories fusion categories? haim kalmanWeb在 multitensor 的基础上再要求半单（semisimple）和有限（finite）的条件，得到多重融合范畴（multifusion category）。 此外，若在前三者基础上有 \mathrm {End}_ {\mathcal C} (\mathbf 1) = \mathbb k ，则去掉“多重”，分别得到环范畴（ring category）、张量范畴（tensor category）和融合范畴（fusion category）。 （感觉真是没有什么好的翻译） … pinselmannWebIn this paper we study a toy categorical version of Lusztig's induction and restriction functors for character sheaves, but in the abstract setting of multifusion categories. Let $\mathscr{C}$ be an indecomposable multifusion category and let $\mathscr{M}$ be an invertible $\mathscr{C}$-bimodule category. Then the center … pinselmanufaktur aulitzkyWebDistortion for multifactor bimodules and representations of multifusion categories Marcel Bischo , Ian Charlesworth, Samuel Evington, Luca Giorgetti, and David Penneys October 5, haim journalisteWebWorking 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 … pinselmarkerWeb25 nov. 2014 · The 3-categories of semisimple 2-categories and of multifusion categories are shown to be equivalent. A weakening of the notion of fusion 2-category is introduced. Multifusion 2-categories are… Expand Highly Influenced View 3 excerpts, cites results and background Save Alert The categorified Grothendieck–Riemann–Roch … pinsel mit tankWebGiven a multifusion 2-category, potentially with some additional levels of monoidality, we prove theorems about the structure of the 2-category obtained by condensing a suitable algebra object. pinsel paint