Neurology Mathematics Ideas70.pdf - Thus in T(J\u03ba there is a distinguished object given by the pre-image of the identity functor R a\u2208A a \u22a0[\u03ba a \u2208

Neurology Mathematics Ideas70.pdf - Thus in T(Ju03ba there...

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Thus in T( J κ ) there is a distinguished object, given by the pre-image of the identity functor in L ex A , A ( I 0 , I 0 ) under the equivalence (5.25). It is given explicitly by integraltext a ∈A a [ κ ] a T( J κ ), with balancing determined by the one of integraltext a ∈A a a . (iii) Similarly, for the defect one-manifolds that coincide with J κ as manifolds, but have general framings, i.e. with general indices κ and κ , the gluing category is canonically equivalent to L ex A , A ( I κ 0 , I κ 0 ). If κ = κ , then this functor category is equivalent to the Drinfeld center and is thus monoidal; if κ κ = 2, then it is equivalent to the category of objects x ∈ A together with coherent natural isomorphisms a x = x a ∨∨ for all a ∈ A , which is in general not monoidal (e.g., the monoidal unit of A might not have the structure of an object in this category). The categories for all other cases are equivalent to one obtained for the latter two cases, determined by κ κ
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