Definition:Category of Monoids
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Definition
The category of monoids, denoted $\mathbf{Mon}$, is the metacategory with:
Objects: | monoids | |
Morphisms: | monoid homomorphisms |
Note
The reason to call $\mathbf{Mon}$ a metacategory is foundational; allowing it to be a category would bring us to axiomatic troubles.
Also see
- Category of Monoids is Category
- Definition:Category of Monoid Categories
- Results about the category of monoids can be found here.
Sources
- 2010: Steve Awodey: Category Theory (2nd ed.) ... (previous) ... (next): $\S 1.4.13$