Spherical categories

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August undefined, 2024

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 … 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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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... nightfall star wars

algebraic geometry - Spherical objects in Derived …

Webcategory 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 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). 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 ... night falls song nightcore

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[hep-th/9310164] Spherical Categories - arXiv.org

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) 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 … nightfall stats destiny 2WebAug 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 … nightfalls studios

"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

category theory - Spherical fusion categories: A certain …

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 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 ...

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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 WebJun 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...

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 … 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

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 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 ...

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 …

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. [1] Spherical fusion … np to aucklandWebAnnals of Mathematics Annals of Mathematics, Journal nptofWebMay 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 … npt nps threadsWebFeb 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). npt nuclear weapons statesWebApr 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. night falls textWebFeb 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). npt objectivesWebApr 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 … npt nptf threads