Example 9.2.3.1.1 (00WN): Monoids as One-Object Categories

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We have an isomorphism of categories¹

via the delooping functor

B : Mon \to Cats

, exhibiting monoids as exactly those categories having a single object.

¹This can be enhanced to an isomorphism of

2

-categories

between the discrete

2

-category

{Mon}_{2 disc}

Mon

and the

2

-category of pointed categories with one object.

Proof of Example 9.2.3.1.1.

Omitted.

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