Category:Definitions/Morphism Categories

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This category contains definitions related to Morphism Categories.
Related results can be found in Category:Morphism Categories.

Let $\mathbf C$ be a metacategory.

Its morphism category, denoted $\mathbf C^\to$, is defined as follows:

Objects:         The morphisms $\mathbf C_1$ of $\mathbf C$
Morphisms: $g: f \to f'$ is a pair $\tuple {g_1, g_2}$ of morphisms of $\mathbf C$ such that $g_2 \circ f = f' \circ g_1$
Composition: $\tuple {h_1, h_2} \circ \tuple {g_1, g_2} := \tuple {h_1 \circ g_1, h_2 \circ g_2}$, whenever this is defined
Identity morphisms: $\operatorname{id}_f := \tuple {\operatorname{id}_C, \operatorname{id}_D}$ for $f: C \to D$

Pages in category "Definitions/Morphism Categories"

The following 3 pages are in this category, out of 3 total.