Spherical categories

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August undefined, 2024

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 15, 2016 · Triangulated categories generated by w-spherical objects. Let k be an algebraically closed field. Let T be a k-linear triangulated category and w ∈ Z. An object s of T is called w-spherical [32] if it satisfies the following axioms: (S1) it is a w-spherelike object [18], i.e. Hom T (s, Σ i s) = {k if i = 0, w; 0 otherwise, and (S2)

[1011.0707] Orthogonally spherical objects and spherical fibrations

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! 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 criscilla crossland cancer

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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 … 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 … 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 … crisci nunzio

3-Dimensional TQFTs from non-semisimple modular categories

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 … WebFeb 3, 2024 · The 2-category of monoidal categories 7. Properties 8. Coherence 9. Closure 10. Relation to multicategories 11. Internal logic 12. Scalars 13. Where the definition comes from 14. Relation to lax functors, orientals and descent 15. Remark: pseudo versus lax, orientals versus unorientals 16. Variants 17. Related concepts 18. References Idea 0.1 manatt medicaidWebFUKAYA CATEGORIES OF SURFACES, SPHERICAL OBJECTS, AND MAPPING CLASS GROUPS DENIS AUROUX AND IVAN SMITH Abstract. We prove that every spherical object … manat to dollar

"WebNov 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 … " - Spherical categories

Spherical categories

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 ... 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 …

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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 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 …

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... 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 …

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 … 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 …

WebJan 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 …

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 … crisci mario metzWebcategory 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 manatt llcWebJan 16, 2024 · Based on the shape of the bacterial cell, bacteria can be mainly classified into four major categories, namely: Spherical bacteria or Coccus Rod-shaped bacteria or Bacillus Spiral bacteria Filamentous bacteria. Apart from these four main categories, there are other odd-shaped bacteria such as the following shapes, namely: criscin manatua promotionsWebIn 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 manattoWebApr 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. crisci mattonelleWebJun 7, 2024 · spherical category. ribbon category, a.k.a. tortile category. compact closed category. With duals for morphisms. monoidal dagger-category? symmetric monoidal … manatv classes