Around 7:30 in the video, we learn about discrete categories, and that a monoid can be considered a discrete monoidal category.

"A category is called discrete when all of its morphisms are identities."

This leaves me a little confused. The morphisms on a monoid are *not* generally all identities, right? A monoid has one object, and if it's morphisms were only identities, that would be give you just the 1 category.

Maybe you have to think of the objects of the discrete monoidal category from a monoid as the *morphisms* of the original monoid?