Proposition (Parameterized dinaturality)
(for
f :
Z
U(B)
U(A)
and
g :
X
U(A)
Y
U(B)
in C):
| = | ||
Tr(X Z) Y A
((idX
symmZ U(A));
(g
idZ);
(idY
(symmU(B) Z);
f)))
| = |
Tr(X Z) Y B
((idX
f);
g)
|
| = | (Yanking) | |
| = | (Naturality of Tr) | |
| = | (Naturality of symm) | |
| = |
(Functoriality of )
| |
| = | (Symmetry sliding) | |
| = | (Naturality of symm) | |
| = | (Naturality of Tr) | |
| = | (Yanking) |