Proposition (Q is State(D)). Q is isomorphic to State(D).
[[_]]D : | LGraph(Mix(C,P)) | ![]() |
D |
![]() |
![]() |
||
[[_]]Q : | State(LGraph(Mix(C,P))) | ![]() |
Q |
We will now define an identity-on-objects isomorphism between Q and State(D):
By definition, G : XS
YS
in LGraph(Mix(C,P))
and so define:
which gives us:
By definition, G : X
Y
in State(LGraph(Mix(C,P)))
and so define:
It is routine to show that st and ts are symmetric premonoidal functors, and
that they form an isomorphism.