Coend (Category Theory)

Let $\mathcal{C},\mathcal{D}$ be categories.
Let $F,G:{\mathcal{C}}^{op}\times \mathcal{C}\to \mathcal{D}$ be bifunctors.
A dinatural transformation is a natural transformation between bifunctors.
A coend is a an initial co-wedge $\tau :CoWedge\mathcal{D}F$.

Remarks

Note that $F,G$ are called Profunctor when $\mathcal{D}=\mathbf{Set}$.

Sources

Ends and Coends
loregian2023-coend-calculus
yoneda1960-end

See also

End (Category Theory)