This is perhaps an ill-proposed question. Any way, thank you guys.

We have a lot of bi-stuffs, such as bi-module, bi-bundle, etc. They are basically two commuting actions from two sides, left and right. This is somehow related to we are writing horizontally. If we are writing vertically, people may talk top module, under module.

I am wondering if we have three (or 4, any other) actions on a object by three different things. Imaging We have a triangle, acted on tree side. Is it possible to keep them compatible in a reasonable nice way? The uninteresting way is they are mutually commutative. If one can define an "tri-module", is it just un-useful toy?