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Spherical categories

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 … WebApr 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).

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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 ... 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 stiginey https://steve-es.com

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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 … 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. 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 … stiggy\u0027s dogs michigan

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Spherical categories

The UK’s ST40 Spherical Tokamak Achieves Crucial Plasma …

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 … 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.

Spherical categories

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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 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 …

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

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 … 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 …

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

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 stigho electroWebJan 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: stigho electro b.vWebFeb 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 … stigh on eyelid