Some of you might be familiar with (.:) = (.) . (.).

It has type :: (c -> d) -> (a -> b -> c) -> a -> b -> d

First of all, I always called it "dot". Don't know where I picked that one up, though. (.:) looks like it could conflict with some lens or something. Would need checking.

Also, which version? This simple one? Or the Category one?

    (.).(.) :: (Category cat) => cat c d -> (a -> cat b c) -> a -> cat b d

I know little about Category Theory, but throwing together some random words I collected over time that looks like... a "contravariant bind in the monad of endocategories", maybe? I just invented that and it's almost certainly meaningless gibberish, but knowing our community it might well be that there's a lib for that.

Also, why is

    h = f .: g == (f .) . g

not good enough?

So many questions, so much bikeshedding to do, so little time...