  This article is motivated by the need for better understanding of refined
Riemann-Roch theorems and the behavior of the determinant of the cohomology.
This poses a certain problem of functoriality and can be understood as that of
giving refined constructions of operations in algebraic $K$-theory. In this
article this is specialized to mean refining the excess formula, which measures
the failure of base change, to the level of Deligne's virtual category. We give
a natural set of properties for such a refinement, and prove that there exists
a unique family of excess formulas on this refined level satisfying these
properties.
