Definition:Category of Cocones

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Let $\mathbf C$ be a metacategory.

Let $D: \mathbf J \to \mathbf C$ be a $\mathbf J$-diagram in $\mathbf C$.

The category of cocones from $D$, denoted $\map {\mathbf {Cocone} } D$, is the category with:

Objects:         cocones to $D$
Morphisms: morphisms of cocones
Composition: Composition in $\mathbf C$
Identity morphisms: $\operatorname{id}_{\struct {C, c_j} } := \operatorname{id}_C$, for a cocone $\struct {C, c_j}$

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