2024 Spherical categories

Spherical categories

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WebApr 3, 2024 · There is a difference between strictly spherical objects (i.e., complexes of projectives which are concentrated in a single degree) and spherical objects in your sense … WebJun 7, 2024 · Claim and status. In condensed matter theory it is folklore that species of anyonic topological order correspond to braided unitary fusion categories / modular tensor categories. The origin of the claim may be: Alexei Kitaev, Section 8 and Appendix E of: Anyons in an exactly solved model and beyond, Annals of Physics 321 1 (2006) 2-111.

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WebMar 1, 2024 · This is noted in Cockett 1993, p. 280, also Corollary 5.9, where Bob Walters and Shu-Hao Sun? are named as advocates of this method. (However, note that Cockett does not insist on an initial object.) In particular, then, the free distributive category, which is the free distributive category on the empty category, is the category of finite sets, up to … WebJun 19, 2016 · Spherical fusion categories: A certain functor 1. Context Let C be a spherical fusion category over an algebraically closed field k of characteristic zero. Denote by V e c the category of finite-dimensional vector spaces. Currently, I am ... category-theory monoidal-categories natural-transformations topological-quantum-field-theory cassava variety

Lucite Globe: Spherical Concepts, Inc. Frazer, PA USA MCMXCI …

WebAnnals of Mathematics Annals of Mathematics, Journal Webthe category of vector spaces, based on spherical categories. The category Algis proposed by Habiro to be isomorphic to the cobor-dism category of once-punctured surfaces. If the proposal is proved valid, the result of this paper would imply a construction of a TQFT functor based on a spherical category. 1. Introduction WebOct 25, 1993 · Spherical Categories. This paper is a study of monoidal categories with duals where the tensor product need not be commutative. The motivating examples are categories of representations of Hopf algebras and the motivating application is the … SPHERICAL CATEGORIES John W. Barrett & Bruce W. Westbury 10 August 1993; … Hep-Th 9310164V2 - [hep-th/9310164] Spherical Categories - arXiv.org cassavant

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WebApr 1, 2024 · A based presentation of a (small) spherical based tensor category ( C, X) is a set of morphisms F between tensor powers of X, and a set of relations R satisfied in C such that C ≅ C ( F) / R ‾ where C ( F) is the free (based, strictly pivotal and strict monoidal) spherical C -linear monoidal category (possibly not abelian and with non-simple … WebApr 25, 2012 · A spherical category is a piv otal one where the left and righ t traces coincide. Thus, Rep H is a spherical category, whenever H is a spherical Hopf algebra. Remark 2.3. cassava vs yuca rootWebApr 3, 2024 · Lets denote by C n the category of n -spherical objects in C. If I an not wrong C n is a waldhausen category where weak equivalences are quasi-iso and cofibrations are ordinary cofibrations such that the cofiber is also an object in C n. Now the Wladhausen theorem says that h o c o l i m n K ( C n) ∼ K ( C). casse auto ain mlila kia

"WebFeb 3, 2024 · Apparently, an example of a pivotal non-spherical category can be found in the world of Hopf algebras/representation theory: Let $(H, \omega)$ be a pivotal non-spherical Hopf algebra with pivot $\omega$ (see From Hopf algebras to tensor categories by Andruskiewitsch et al. for an example). " - Spherical categories

Spherical categories

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WebFind many great new & used options and get the best deals for Lucite Globe: Spherical Concepts, Inc. Frazer, PA USA MCMXCI (1991) at the best online prices at eBay! Free shipping for many products! WebNov 5, 2024 · In a spherical fusion category C, an equivariant indicator of an object in C is defined as a functional on the Grothendieck algebra of the quantum double Z(C) via generalized Frobenius-Schur ...

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WebNov 2, 2010 · Orthogonally spherical objects and spherical fibrations. Rina Anno, Timothy Logvinenko. We introduce a relative version of the spherical objects of Seidel and Thomas. Define an object E in the derived category D (Z x X) to be spherical over Z if the corresponding functor from D (Z) to D (X) gives rise to autoequivalences of D (Z) and D … WebMay 10, 1999 · In the third section we define spherical Hopf algebras so that the category of representations is spherical. Examples of spherical Hopf algebras are involutory Hopf …

WebFeb 15, 2024 · The last result of this section, Theorem 4.13, pertains to spherical fusion categories. Sphericality is a very weak assumption as all known examples of fusion categories possess a spherical structure. We prove that if C is a spherical fusion category with a formal codegree f of square-free norm, then f ∈ Z or f = (1 / 2) (5 ± 5). WebMay 10, 1999 · The motivating examples are categories of representations of Hopf algebras. We introduce the new notion of a spherical category. In the first section we prove a coherence theorem for a monoidal category with duals following S. MacLane (1963,Rice Univ. Stud.49, 28–46). In the second section we give the definition of a spherical …

WebFeb 2, 2024 · Idea. There are many ways to describe a * *-autonomous category; here are a few:. it is a monoidal category in which all objects have “duals”, but in a weaker sense than in a compact closed category.; it is a closed monoidal category in which the internal-hom can be expressed in terms of the tensor product in a particular way.; it is a linearly distributive … WebAug 22, 2024 · We compute the fusion rule of a one-parameter family of spherical categories constructed by one author from the classification of singly generated …

WebFeb 3, 2024 · Given a morphism φ ∈ H o m C ( X, Y) the (strict) pivotal structure lets one "pivot" its representing string diagram (turn its arrows around): Here we make use of the identification X ∗ ∗ = X. (The expression X ∗ is not ambigous because a right rigid pivotal category is left rigid, and left and right dual objects of a given object ...

WebIn category theory, a branch of mathematics, a spherical category is a pivotal category in which left and right traces coincide. Wikiwand is the world's leading Wikipedia reader for … cassava vs yucaWebMay 10, 1999 · Four dimensional topological quantum field theory, hopf categories, and the canonical bases J. Math. Phys. , 35 ( 1994 ) , pp. 5136 - 5154 View in Scopus Google … cassave maken cassavainWebJan 1, 2024 · As noted in Table 2, data from these three sources show slight variability when looking at the soft spherical category (prescribing range 50% to 56%) and more consistency with torics and cosmetics. TABLE 2 2024 CONTACT LENS SPECTRUM , ABB OPTICAL GROUP, AND GFK RETAIL AND TECHNOLOGY DATA FOR U.S. SOFT LENSES IN TERMS … casse auto jamot sainteWebJun 7, 2024 · spherical category. ribbon category, a.k.a. tortile category. compact closed category. With duals for morphisms. monoidal dagger-category? symmetric monoidal … cassavesoep met kokosmelkWebJan 23, 2024 · Spherical fusion categories: A certain functor. Ask Question. Asked 2 years, 2 months ago. Modified 1 year, 5 months ago. Viewed 128 times. 3. 1. Context. Let be a … casse haon saint just malmontWebcategory Cone may construct thede-equivariantization C G of Fun(G)-modules, where Fun(G) 2Rep(G) is the regular algebra and G is a nite group. IC G is G-graded. IdimC G = dim(C)=jGj IIf Cis braided and DˆC0then C G is braided. Lemma Let Cbe a pre-modular category, and Rep(G) ˘=TˆC0be the maximal, Tannakian, central subcategory.Then C G is either casse jacky