Definition:Cone (Category Theory)

Definition

Let $\mathbf C$ be a metacategory.

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

A cone to $D$ comprises an object $C$ of $\mathbf C$, and a morphism:

$c_j: C \to D_j$

for each object of $\mathbf J$, such that for each morphism $\alpha: i \to j$ of $\mathbf J$:

$\begin{xy}\[email protected][email protected]+2px{ C \ar[d]_*+{c_i} \ar[dr]^*+{c_j} \\ D_i \ar[r]_*+{D_\alpha} & D_j }\end{xy}$

is a commutative diagram.

This article is complete as far as it goes, but it could do with expansion.
In particular: when time comes, add def "cone is natural trafo $\kappa_C \to D$ with $\kappa_C$ constant functor"
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