Definition:Category with Products/Binary
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Definition
Let $\mathbf C$ be a metacategory.
Then $\mathbf C$ is said to have binary products or to be a (meta)category with binary products if and only if:
- For all objects $C, D \in \mathbf C_0$, there is a binary product $C \times D$ for $C$ and $D$.
Examples
- The category of sets $\mathbf{Set}$ (proof)
- The category of categories $\mathbf{Cat}$ (proof)
Sources
- 2010: Steve Awodey: Category Theory (2nd ed.) ... (previous) ... (next): $\S 2.6$