Generalization of natural transformationsIn category theory , a branch of mathematics , a dinatural transformation
α
{\displaystyle \alpha }
functors
S
,
T
:
C
o
p
×
C
→
D
,
{\displaystyle S,T:C^{\mathrm {op} }\times C\to D,}
written
α
:
S
→
¨
T
,
{\displaystyle \alpha :S{\ddot {\to }}T,}
is a function that to every object
c
{\displaystyle c}
C
{\displaystyle C}
α
c
:
S
(
c
,
c
)
→
T
(
c
,
c
)
{\displaystyle \alpha _{c}:S(c,c)\to T(c,c)}
D
{\displaystyle D}
and satisfies the following coherence property : for every morphism
f
:
c
→
c
′
{\displaystyle f:c\to c'}
C
{\displaystyle C}
commutes.
The composition of two dinatural transformations need not be dinatural.
See also
References
Mac Lane, Saunders (2013). Categories for the working mathematician . Springer Science & Business Media. p. 218.
External links
Categories :
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