Definition:Discrete Category
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Definition
Let $\CC$ be a metacategory.
Then $\CC$ is said to be discrete if and only if it comprises only identity morphisms.
If the collection $\CC$ constitutes the objects of $\mathbf C$, then $\mathbf C$ may also be denoted $\map {\mathbf {Dis} } \CC$.
Also see
- Results about discrete categories can be found here.
Sources
- 2010: Steve Awodey: Category Theory (2nd ed.) ... (previous) ... (next): $\S 1.4.12$