Double categories and quantum groupoids

Nicolas Andruskiewitsch; Sonia Natale

Double categories and quantum groupoids

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arxiv math/0308228 v2 pith:KNIT25Z4 submitted 2003-08-25 math.QA

Nicolas Andruskiewitsch , Sonia Natale This is my paper · ORCID

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We give the construction of a class of weak Hopf algebras (or quantum groupoids) associated to a matched pair of groupoids and certain cocycle data. This generalizes a now well-known construction for Hopf algebras, first studied by G. I. Kac in the sixties. Our approach is based on the notion of double groupoids, as introduced by Ehresmann.

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Pita factorisation in operadic categories
math.CT 2025-12 conditional novelty 6.0 of 10

For strictly factorisable operadic categories, the pita nerve is a coherent top-lax simplicial category, and a decomposition space when all quasibijections are invertible.

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