I will introduce generalized functions and show how they can be used to reinterpret and generalize causal models and the causal relations that they express in a variety of different ways. As a first step, I define generalized functions and their compositions as natural generalizations of multi-valued functions. I then proceed to show how nondeterministic structural causal models can be expressed using generalized functions, and present two novel types of model reduction that this allows. Generalizing these two kinds of reductions results in two definitions of causal abstraction: the first generalizes our earlier definition of abstraction to nondeterministic models, the second captures the idea of a partial abstraction.