  In this article we note that in a number of situations the operator product
and the classical action satisfy a natural compatibility condition. We consider
the interest of this condition to be twofold: First, the naturality
(functoriality) of the compatibility condition suggests that it be used for
geometrical applications of renormalized functional integration. Second, the
compatibility can be used as the definition of a category; consideration of
this category as the central object of study in quantum field theory seems to
have quite some advantages over previously introduced theories of the type
``S-matrix theory'', ``Vertex operator algebras'', since this seems to be the
only category in which both the action and the expectation values enter, the
two being linked roughly speaking by a combination of the Frobenius property
and the renormalized Schwinger-Dyson equation.
