Incategory theory, a branch ofmathematics, adinatural transformation${\displaystyle \alpha }$ between twofunctors

${\displaystyle S,T:C^{\mathrm{o}\mathrm{p}}\times C\to D,}$

written

${\displaystyle \alpha :S\ddot{\to }T,}$

is a function that to every object${\displaystyle c}$ of${\displaystyle C}$ associates an arrow

${\displaystyle {\alpha }_c:S(c,c)\to T(c,c)}$ of${\displaystyle D}$

and satisfies the followingcoherence property: for every morphism${\displaystyle f:c\to c^{\prime }}$ of${\displaystyle C}$ the diagram

commutes.^[1]

The composition of two dinatural transformations need not be dinatural.

• Extranatural transformation
• Natural transformation

• Fosco, Loregian (22 July 2021),(Co)end Calculus, Cambridge University Press,arXiv:1501.02503,doi:10.1017/9781108778657,ISBN 9781108746120,S2CID 237839003
• Dubuc, Eduardo; Street, Ross (1970). "Dinatural transformations".Reports of the Midwest Category Seminar IV. Lecture Notes in Mathematics. Vol. 137. pp. 126–137.doi:10.1007/BFb0060443.ISBN 978-3-540-04926-5.

• dinatural transformation at thenLab

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