Abstract
In this paper we give necessary and sufficient conditions for a comodule magma over a weak Hopf quasigroup to have a total integral, thus extending the theories developed in the Hopf algebra, weak Hopf algebra and non-associative Hopf algebra contexts. From this result we also deduce a version of Maschke’s theorems for right (H, B)-Hopf triples associated to a weak Hopf quasigroup H and a right H-comodule magma B.
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