  For any acyclic quiver, we establish a family of structure isomorphisms for
its cohomological Hall algebra (CoHA). The family is parameterized by
partitions of the quiver into Dynkin subquivers. For each such partition, we
write the domain of our isomorphism as a tensor product of subalgebras in two
ways. In the first, each tensor factor is isomorphic to the CoHA of the quiver
with a single vertex and no arrows. In the second, the tensor factors are each
isomorphic to the CoHAs of the corresponding Dynkin subquivers. When the quiver
is already an orientation of a simply-laced Dynkin diagram, our results
interpolate between isomorphisms proved by Rimanyi. Such CoHA decompositions
appear in prior work of Davison--Meinhardt and Franzen--Reineke, but our proof
gives an explicit topological realization of these results. As a consequence of
our method, we deduce that certain structure constants in the CoHA naturally
arise as CoHA products of classes of Dynkin quiver polynomials.
