Probability sheaves

In probability theory, random elements are maps from a sample space Omega to a value space A. The sample space carries the randomness, and this is propagated along the map to A. Importantly, the precise choice of sample space is irrelevant, and probabilistically meaningful properties are invariant under change of sample space.

Probability sheaves are mathematical structures whose elements may be thought of as "abstract random elements" independent of any specific sample space representation. In the talk, I shall introduce this notion, using simple examples to illustrate it, and I shall explore the interaction between probability theory and category-theoretic structure on the category of probability sheaves.