Spherical categories

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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 … 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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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 ... 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 … cherry creek denver co restaurants

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WebIn category theory, a branch of mathematics, a spherical category is a pivotal category (a monoidal category with traces) in which left and right traces coincide. Spherical fusion … WebA spherical category is deﬁned to be a pivotal category which satisﬁes an extra condition, which states that two trace maps are equal. The universal strict pivotal category has an … WebJan 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 … cherry creek dentist office

Classification of spherical fusion categories of Frobenius-Schur ...

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 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 … cherry creek denver condosWebApr 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 … cherry creek denver converse shoes

"WebFUKAYA CATEGORIES OF SURFACES, SPHERICAL OBJECTS, AND MAPPING CLASS GROUPS DENIS AUROUX AND IVAN SMITH Abstract. We prove that every spherical object … " - Spherical categories

Spherical categories

The UK’s ST40 Spherical Tokamak Achieves Crucial Plasma …

WebIn any spherical category, the (quantum) dimension of an object Xis the endomorphism of the monoidal identity object given by dim(X) = tr(1 X), the trace of its identity map. In the case of a spherical fusion category over K, it may be regarded as an element of the eld K. The dimension of a spherical fusion category Cis C:= X X2S C dim(X)2 where S WebIn a spherical category, left trace equals right trace, so a closed graph can be drawn on a sphere. If it is spherical, rigid, and semisimple, then you can use the graph of a …

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WebApr 11, 2024 · April 11, 2024. As the race towards the first commercially viable nuclear fusion reactor heats up, the UK-based Tokamak Energy has published a paper on its recent achievements with its ST40 ... WebAnnals of Mathematics Annals of Mathematics, Journal

WebApr 1, 2024 · The first is based on modular categories see [33,36,6] and the second is based on spherical categories see [37,8]; these constructions are related in [38]. Later the first approach has been... WebJun 23, 2024 · Spherical objects in Derived categories. Let D b ( X) is the derived category of coherent sheaves on the smooth projective variety X and an object E ∈ D b ( X) is …

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). 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 …

WebFeb 28, 2024 · The variable ‘vdata’ that i loaded from my m file has two columns,the first is x and the second is y.I'm supposed to Use the nonlinear least-square tool ‘lsqcurvefit’ to estimate the two parameters ‘a’ and ‘c’, and fit a function of the form: y = c[1.5(x/a) - 0.5(x/a)^3] if x < a and y = c if x >= a

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 … flights from sri lanka to malaysiaWebJun 1, 2007 · In the present article, we develop the notions of trialgebra and cotrialgebra, generalizations of Hopf algebras with two multiplications and one comultiplication or vice versa, and the notion of... cherry creek dental artsWebNov 5, 2024 · We classify spherical fusion categories of Frobenius-Schur exponent 2 up to monoidal equivalence. We also classify modular categories of Frobenius-Schur exponent … flights from sri lanka to thailandWebApr 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). flights from sps to new yorkWebFind 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! flights from srq to atlWebFind 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 … flights from sps to dallasWebJun 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. flights from sps to dfw