Proof of trace respecting double symmetry
Proposition (Trace respects double symmetry)
(for
f
:
V
W
and
g
:
X
U A
Y
U A
in
C
):
=
Tr
X Y A
(
g
)
f
=
Tr
(X
V) (Y
W) A
((
id
X
symm
V U(A)
); (
g
f
); (
id
Y
symm
U(A) W
))
Proof.
=
(Acyclic graph iso)
=
(Strength of Tr)
=
(Naturality of Tr)
=
(Acyclic graph iso)
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