> **Puzzle.** What is the category with \$$\mathbf{M}\$$ as its only object and functors from \$$\mathbf{M}\$$ to itself as morphisms?

Such a category with morphisms being functors from a category to itself would be the category of [endomorphisms](https://ncatlab.org/nlab/show/endomorphism) of \$$\mathbf{M}\$$.

Endo- comes from the Greek, ἔνδον [endon] meaning "within, inner, absorbing, or containing".