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While building a purely functional data structure library for personal fun and professional use, and while using other libraries, I found that the "Fantasy Land Specification" was mentioned from time to time. They use this hierarchy. Although I did read some about category theory (tried and failed to fully understand all the concepts), some of the terms used in the specification are unknown to me (like Chain, Apply). My question:
I think of this as the "semigroupoid" factoring. Here's the canonical Haskell library, with an explanation of why the extra classes exist: https://hackage.haskell.org/package/semigroupoids. In this library, fantasyland's Chain is called Bind.