The library should model that a Group induces a Groupoid

[Blaisorblade]

Like a Semigroup induces a Semigroupoid, a Group induces a Groupoid.
The first relation is captured by the instance: Semigroup m => Semigroupoid (Semi m) (link to Hackage docs), but there is no such relationship defined. It would be something like:

instance Group m => Groupoid (Semi m) where
  inv (Semi n) = Semi (groupInv m)

I'm also missing a definition of Group among your packages.

I'm not asking this just so, but because I've run into an application where some concepts are naturally modeled using groupoids and groups (even though I'd need a slightly different definition).

[ekmett]

algebra supplies a group class, but is rather deeply unsuitable to this purpose.