  A natural transformation $\mathfrak{J}$ between functors valued in the
category $\mathfrak{Chdv}_{0}$ is assembled. $\mathfrak{Chdv}_{0}$ is obtained
by replacing both the categories $\mathrm{ptls}$ and $\mathrm{ptsa}$ with the
category of topological linear spaces in the defining properties of the
category $\mathfrak{Chdv}$ introduced in one of our previous papers. By letting
a $\mathfrak{dp}$-valued functor be (classical) quantum whenever every its
value is a dynamical pattern whose set map takes values in the set of
(commutative) noncommutative topological unital $\ast-$algebras, and letting a
(classical) quantum $0$-species be a $\mathfrak{Chdv}_{0}$-valued functor
factorizing through the canonical functor from $\mathfrak{dp}$ to
$\mathfrak{Chdv}_{0}$ into a (classical) quantum $\mathfrak{dp}$-valued
functor, we have that the domain and codomain of $\mathfrak{J}$ are a classical
and a quantum $0$-species respectively.

Functional Analysis