Definition:Category of Cones
Jump to navigation
Jump to search
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 cones to $D$, denoted $\mathbf{Cone} \left({D}\right)$, is defined as follows:
Objects: | The cones to $D$ | |
Morphisms: | The morphisms of cones | |
Composition: | Composition in $\mathbf C$ | |
Identity morphisms: | $\operatorname{id}_{\left({C, c_j}\right)} := \operatorname{id}_C$, for a cone $\left({C, c_j}\right)$ |
Also see
Sources
- 2010: Steve Awodey: Category Theory (2nd ed.) ... (previous) ... (next): $\S 5.4$: Definition $5.15$