> **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".

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".