Abstract:

The aim of this paper is to define and study the Smash product of two bimonads. Assume that F and G are bimonads, GF denotes their Smash product, the monoidal structure of GF was discussed via the theory of 2category. We showed that the bimonad structure of GF is equivalent to the monoidal structure of GFmodules. Finally, we gave necessary and sufficient conditions for the category of GFmodules to be a monoidal category.

Key words: bimonad, Smash product, monoidal category, 2category