Dinatural transformation explained

In category theory, a branch of mathematics, a dinatural transformation

\alpha between two functorsS,T : C ^{op} x C\to D,

written

\alpha : S\ddot\to T,

is a function that to every object

c of C associates an arrow\alpha _{c} : S(c,c)\to T(c,c) of D

and satisfies the following coherence property: for every morphism

f:c\to c' of C the diagramcommutes.^[1]

The composition of two dinatural transformations need not be dinatural.

See also

• Extranatural transformation
• Natural transformation

Notes and References

1. Book: Mac Lane . Saunders . Saunders Mac Lane. Categories for the working mathematician . 2013 . Springer Science & Business Media . 218.