Definition:Category of Cocones

Definition

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 $\mathbf{Cocone} \left({D}\right)$, is the category with:

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

Also see

• Category of Cocones is Category
• Definition:Category of Cones
• Definition:Colimit