Algebraic structures in comodule categories over weak bialgebras. Issue 7 (3rd July 2022) - Walton, Chelsea; Wicks, Elizabeth; Won, Robert
Abstract: For a bialgebra L coacting on a k -algebra A, a classical result states A is a right L -comodule algebra if and only if A is an algebra in the category M L of right L -comodules. We generalize this to the setting of weak bialgebras H . We prove that there is an isomorphism between the categories of right H -comodule algebras and the category of algebras in M H . We also recall and introduce the formulaic notion of H coacting on a k -coalgebra and on a Frobenius k -algebra, respectively, and prove analogous category isomorphisms. Many examples are provided throughout.