  The categorical models of the differential lambda-calculus are additive
categories because of the Leibniz rule which requires the summation of two
expressions. This means that, as far as the differential lambda-calculus and
differential linear logic are concerned, these models feature finite
nondeterminism and indeed these languages are essentially non-deterministic. We
introduce a categorical framework for differentiation which does not require
additivity and is compatible with deterministic models such as coherence spaces
and probabilistic models such as probabilistic coherence spaces. Based on this
semantics we sketch the syntax of a deterministic version of the differential
lambdacalculus.
