Idea
A dinatural transformation is a weaker form of natural transformations used in the definition of coends and ends.
Definition
Let be a categories. Let be bifunctors. A dinatural transformation between F and G is given by,
\alpha_{c} : F(c,c)\to_D G(c,c) \qquad \forall c:C $$ Such that for each pair $c,c':C$ the hexagon commutes:G(idc,f)∘αc∘F(f,idc)=G(f,idc′)∘αc′∘F(idc′,f).
## Remarks Note that this is weaker than a [[natural transformation]] between $F$ and $G$, since that would require morphisms for all pairs rather than just the diagonal maps. ## See also [[Profunctor]] ## Sources - [[gylterud2011-symmetric-containers-thesis]] - https://ncatlab.org/nlab/show/dinatural+transformation