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.
Categories: math.FA