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Sure, I don't disagree. I've bashed my head countless times against short, super-abstract definitions for which it is very difficult to provide concrete examples. So I totally empathize with the feeling you express.

However:

(0) As for “endomorphism”, the definition “function with the same domain and codomain” should be pretty easy to understand to anyone. (Technically, in an arbitrary category, morphisms don't have to be functions, but Haskellers work in the category Hask, whose morphisms are terminating functions.)

(1) The right place to define what a monoid is is the definition of the class Monoid, not the definition of every type that happens to have a Monoid instance.



Haskellers work in the category Hask, whose morphisms are terminating functions

This is my favourite haskellism so far in this thread.




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