Multiplier Hopf coquasigroup: Definition and Coactions

This paper uses Galois maps to give a definition of generalized multiplier Hopf coquasigroups, and give a sufficient and necessary condition for a multiplier bialgebra to be a regular multiplier Hopf coquasigroup. Then coactions and Yetter-Drinfeld quasimodules of regular multiplier Hopf coquasigroups are also considered.