Let $\mathbf C$ be a metacategory.
Let $D: \mathbf J \to \mathbf C$ be a $\mathbf J$-diagram in $\mathbf C$.
- $c_j: D_j \to C$
is a commutative diagram.
Also known as
Some authors, notably Saunders Mac Lane, dislike the name cocone and rather speak of cones from the base $D$.
Cones are then called cones to the base $D$.
So as to avoid the unavoidable ambiguity this gives rise to, on this web site, cocone is the designated term.