  Causal spaces have recently been introduced as a measure-theoretic framework
to encode the notion of causality. While it has some advantages over
established frameworks, such as structural causal models, the theory is so far
only developed for single causal spaces. In many mathematical theories, not
least the theory of probability spaces of which causal spaces are a direct
extension, combinations of objects and maps between objects form a central
part. In this paper, taking inspiration from such objects in probability
theory, we propose the definitions of products of causal spaces, as well as
(stochastic) transformations between causal spaces. In the context of
causality, these quantities can be given direct semantic interpretations as
causally independent components, abstractions and extensions.
