Comodules over weak multiplier bialgebras. (Q2874714)

Weak multiplier bialgebras were introduced by the author, \textit{J. Gómez-Torrecillas} and \textit{E. López-Centella} [Trans. Am. Math. Soc. (in press)] as a generalization of weak bialgebras. In Section 2 of this paper, the category of comodules is considered. The next section is devoted to the study of integrals for regular weak multiplier bialgebra \(A\) with right full comultiplication. It is shown that there is an isomorphism between the vector space of right integrals of \(A\) and the space of homomorphisms from the comodule \(A\) to the comodule \(R\), the base algebra. Section 4 deals with the particular class of full comodules. There is a faithful functor from the full subcategory of full right \(A\)-comodules to the category of firm \(R\)-bimodules. Moreover, in Section 5, a monoidal structure is constructed for the full subcategory of full right \(A\)-comodules in such a way that the preceding functor is monoidal. The author investigates the dual in the monoidal category of full right \(A\)-comodules, if \(A\) has an antipode, the dual vector space of a finite dimensional right comodule has a left comodule structure and they are duals. Finally, Hopf modules are introduced and a Fundamental Theorem of Hopf modules is shown.