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Lecture 15 - Monoidal categories - David Spivak

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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?
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