Constructs coherent Hopf 2-algebras via Hopf coquasigroups relaxing coassociativity, generalizing prior results, with examples from quasi-coassociative cases and Cayley algebra function algebras.
Strict quantum 2-groups
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abstract
A crossed module is (A,H,d,\la) where d:A\to H is a homomorphism of groups and H acts on A, with conditions leading to a groupoid A\lcross H{\to\atop \to}H as an example of a strict 2-group. We give the corresponding notion of a quantum 2-group where we replace the above by Hopf algebras and introduce a new version of quantum groupoid. The work also suggests a natural notion of braided crossed module where A a braided-Hopf algebra in the braided category Z({}_H\CM) of crossed H-modules, although without the full groupoid picture in this more general case.
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On coherent Hopf 2-algebras
Constructs coherent Hopf 2-algebras via Hopf coquasigroups relaxing coassociativity, generalizing prior results, with examples from quasi-coassociative cases and Cayley algebra function algebras.