Spherical categories
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. 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
Spherical categories
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WebFUKAYA CATEGORIES OF SURFACES, SPHERICAL OBJECTS, AND MAPPING CLASS GROUPS DENIS AUROUX AND IVAN SMITH Abstract. We prove that every spherical object … WebJun 7, 2024 · spherical category. ribbon category, a.k.a. tortile category. compact closed category. With duals for morphisms. monoidal dagger-category? symmetric monoidal …
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 … 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 …
WebAnnals of Mathematics Annals of Mathematics, Journal 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 …
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 …
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 … galaxy a 13 5g phone reviewsWebNov 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 … blackberry blueberry jelly recipeWebJan 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 … blackberry blueberry freezer jelly recipeWebApr 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 … blackberry blueberry vape juiceWebIn 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 … blackberry bluetoothWebFeb 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). blackberry blueberry smoothie recipeWebIn 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 blackberry bluetooth hs655