Agreed. Let me drop some references about the relationship between Haskell and Category Theory that really helped me untangle these concepts, in case it might help others.

[1] Haskell/Category Theory https://en.wikibooks.org/wiki/Haskell/Category_theory#cite_n...

[2] Bauer 2016, "Hask is Not a Category" http://math.andrej.com/2016/08/06/hask-is-not-a-category/

[3] A reddit comment in response to #2, https://www.reddit.com/r/haskell/comments/4wk0gs/hask_is_not...

[4] StackOverflow, "Is Hask even a Category?" https://stackoverflow.com/questions/48485660/is-hask-even-a-...