  In this note we highlight a common origin for many ubiquitous geometric
structures, as well as several new ones by using only the functors of
differential calculus in A.M Vinogradov's original sense, adapted to special
classes of (graded) commutative algebras. Special attention is given to the
particularly simple cases of diole and triole algebras and we show the latter
environment is the appropriate one to describe calculus in vector bundles in
the presence of a vector-valued fiber metric.
