Polyadic tensor categories

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ID: 311723
2022
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Abstract
In chapter 11 we generalize tensor categories and braided tensor categories using the commutativity-to-mediality ansatz, as in chapter 7 for algebras. A polyadic (non-strict) tensor category has an n-ary tensor product as an additional multiplication with n − 1 associators of the arity 2n − 1 satisfying a (n2 + 1)-gon relation, which is a polyadic analog of the pentagon axiom. Polyadic monoidal categories may contain several unit objects, and it is also possible that all objects are units. A new kind of polyadic categories (called groupal) is defined: they are close to monoidal categories, but may not contain units: instead (by analogy with the querelements in n-ary groups) the querfunctor and (natural) functorial isomorphisms, the quertors, are considered. The arity-nonreducible n-ary braiding is introduced and the equation for it is derived, which for n = 2 coincides with the Yang–Baxter equation. Then, analogously to the approach in chapter 7, we introduce ‘medialing’ instead of braiding and construct ‘medialed’ polyadic tensor categories.
Reference Key
persistent_1771691549_6999de1d07442 Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Steven Duplij
Journal science and technology of advanced materials
Year 2022
DOI
10.1088/978-0-7503-2648-3ch11
URL
https://iopscience.iop.org/book/mono/978-0-7503-2648-3/chapter/bk978-0-7503-2648-3ch11.pdf
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