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- noun mathematics A
functorthat mapsa categoryto itself
from Wiktionary, Creative Commons Attribution/Share-Alike License
Next we're going to go looking for monoids in this "endofunctor" category using our above definitions.
This is the "endofunctor" category over Hask, and these arrows are natural transformations.
Thus equipped, "Maybe" can be seen as a monoid in the endofunctor category over Hask.
And that, of course, is what a monad is - a monad over a category 'C' is a (categorical) monoid in the endofunctor category over 'C'.