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Showing 1 to 8 of 8 for “"monoidal categories"”.
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Coherence for categorified operadic theories
… isomorphism. This generalizes the theories of monoidal categories and symmetric monoidal categories, and several related notions defined in the literature. Using this definition, we generalize the result that every monoidal category is monoidally equivalent to a strict monoidal category, and …
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Tensor Categories, Z+-rings, and Grothendieck Rings
… define and prove various properties of abelian categories, monoidal categories and tensor categories. Then, we will show how to define a ring that represents a tensor category, which will be called the Grothendieck Ring, and prove that it constitutes a very specific type of ring called a Z + …
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Autonomous Pseudomonoids
… to the context of autonomous pseudomonoids in monoidal bicategories. Autonomous pseudomonoids were introduced in [13] as generalisations of both autonomous monoidal categories and Hopf algebras. Much of the theory of autonomous pseudomonoids developed in [13] was inspired by the example of …
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Derived algebraic geometry over En̳-rings
… En-rings form a geometric counterpart to En-categories, which are higher topological variants of braided monoidal categories. These spaces further provide a geometric language for the deformation theory of general E, structures. A version of the cotangent complex governs such deformation …
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A Coherent Categorification of the Asymptotic Affine Hecke Algebra
… with respect to an exotic t-structure, and sends monoidal duals of connective objects to coconnective objects. To this end, we construct an explicit complex computing the 2-categorical class map for certain monoidal categories over quotient stacks. We then deduce a (co)connectivity statement for …
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Loop Spaces and Iterated Higher Dimensional Enrichment
… has as a partial goal that of understanding the categories and functors that correspond to loop spaces and their associated topological functors. Progress towards this goal has been advanced greatly by the recent work of Balteanu, Fiedorowicz, Schwänzl, and Vogt who show a direct correspondence …
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Near-Group Categories
We consider the possibility of semisimple tensor categories whose fusion rule includes exactly one noninvertible simple object, so-called near-group categories. Data describing the fusion rule is reduced to an abelian group G and a nonnegative integer k. Conditions are given, in terms of G and k, …
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Generalized Rank Invariant : Structure, Möbius Inversion, and Persistence Diagram
Topological Data Analysis relies on persistent homology to quantify the shape of data. Unlike the one-parameter case, multiparameter persistence modules lack a complete discrete invariant analogous to barcodes, and their classification requires tools that can capture subtle interactions across the …