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A natural transformation $\mathfrak{J}$ between functors valued in thecategory $\mathfrak{Chdv}_{0}$ is assembled. $\mathfrak{Chdv}_{0}$ is obtainedby replacing both the categories $\mathrm{ptls}$ and $\mathrm{ptsa}$ with thecategory of topological linear spaces in the defining properties of thecategory $\mathfrak{Chdv}$ introduced in one of our previous papers. By lettinga $\mathfrak{dp}$-valued functor be (classical) quantum whenever every itsvalue 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 functorfactorizing through the canonical functor from $\mathfrak{dp}$ to$\mathfrak{Chdv}_{0}$ into a (classical) quantum $\mathfrak{dp}$-valuedfunctor, we have that the domain and codomain of $\mathfrak{J}$ are a classicaland a quantum $0$-species respectively.

Construction of a Natural Transformation from a Classical to a Quantum 0-Species