Category:Product Categories
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This category contains results about Product Categories.
Definitions specific to this category can be found in Definitions/Product Categories.
Let $\mathbf C$ and $\mathbf D$ be metacategories.
The product category $\mathbf C \times \mathbf D$ is the category with:
Objects: | $\tuple {X, Y}$, for all $X \in \operatorname {ob} \mathbf C$, $Y \in \operatorname {ob} \mathbf D$ | |
Morphisms: | $\tuple {f, g}: \tuple {X, Y} \to \tuple {X', Y'}$ for all $f: X \to X'$ in $\mathbf C_1$ and $g: Y \to Y'$ in $\mathbf D_1$ | |
Composition: | $\tuple {f, g} \circ \tuple {h, k} := \tuple {f \circ h, g \circ k}$, whenever this is defined | |
Identity morphisms: | $\operatorname {id}_{\tuple {X, Y} } := \tuple {\operatorname {id}_X, \operatorname {id}_Y}$ |
Pages in category "Product Categories"
The following 2 pages are in this category, out of 2 total.