Subsection 9.2.3 (01TU): Monoids as One-Object Categories

Preferences





Font:

PDF Style:

Here's a breakdown of the differences between each PDF style:

Style	Class	Font	Theorem Environments
Style 1	`book`	Alegreya Sans	`tcbthm`
Style 2	`book`	Alegreya Sans	`amsthm`
Style 3	`book`	Arno*	`amsthm`
Style 4	`book`	Computer Modern	`amsthm`

*To be replaced with Linus Romer's Elemaints when it is released.

We have an isomorphism of categories¹

via the delooping functor $\mathsf{B}\colon \mathsf{Mon}\to \mathsf{Cats}$ of

, 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 $\mathsf{Mon}_{\mathsf{2disc}}$ on $\mathsf{Mon}$ and the $2$-category of pointed categories with one object.

Proof of Example 9.2.3.1.1.

Omitted.

Noticed something off, or have any comments? Feel free to reach out!

You can also use the contact form below: