Multiplier Hopf Coquasigroup: Motivation and Biduality

Abstract

Inspired by the multiplier Hopf algebra theory introduced by A. Van Daele, this paper introduces a new algebraic structure, a multiplier Hopf coquasigroup, by constructing the integral dual of an infinite-dimensional Hopf quasigroup with faithful integrals. Then, it shows that the biduality theorem also holds for Hopf quasigroups and multiplier Hopf coquasigroups of the discrete type.