Sorry I mixed-up Module with Bi-module
So that you certainly have two other categories RightModule and LeftModule.
Here I see two possibilities:
1 - Restrict Module to the commutative case and create RightModule and
LeftModule and define:
Module(R) := Bimodule(R,R)
BiModule(L,R) := Join(LeftModule(L), RightModule(R))
2 - Define Module as an alias for LeftModule:
Module(R) := LeftModule(R)
BiModule(L,R) := Join(LeftModule(L), RightModule(R))
In my experience, in the commutative case, we never use the two sided case. EG
if v is in a R-vector space, I always write 3*v and never v*3...
What's your preferred choice ?
Cheers,
Florent
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