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# Lecture 15 - Monoidal categories - David Spivak

edited February 5

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1.

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?

Comment Source: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?