  We give further insights into the weighted Hurwitz product and the weighted
tensor product of Joyal species. Our first group of results relate the Hurwitz
product to the pointwise product, including the interaction with Rota--Baxter
operators. Our second group of results explain the first in terms of
convolution with suitable bialgebras, and show that these bialgebras are in
fact obtained in a particularly straightforward way by freely generating from
pointed coalgebras. Our third group of results extend this from linear algebra
to two-dimensional linear algebra, deriving the existence of weighted Hurwitz
monoidal structures on the category of species using convolution with freely
generated bimonoidales. Our final group of results relate Hurwitz monoidal
structures with equivalences of of Dold--Kan type.
