Abstract
We introduce a new type of categorical object called a hom–tensor category and show that it provides the appropriate setting for modules over an arbitrary hom-bialgebra. Next we introduce the notion of hom-braided category and show that this is the right setting for modules over quasitriangular hom-bialgebras. We also show how the Hom–Yang–Baxter equation fits into this framework and how the category of Yetter–Drinfeld modules over a hom-bialgebra with bijective structure map can be organized as a hom-braided category. Finally we prove that, under certain conditions, one can obtain a tensor category (respectively a braided tensor category) from a hom–tensor category (respectively a hom-braided category).
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Communicated by D.N. Yetter.
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Panaite, F., Schrader, P.T. & Staic, M.D. Hom–Tensor Categories and the Hom–Yang–Baxter Equation. Appl Categor Struct 27, 323–363 (2019). https://doi.org/10.1007/s10485-019-09556-y
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DOI: https://doi.org/10.1007/s10485-019-09556-y