It is shown how the theory of commutative monads provides an axiomatic framework for several aspects of distribution theory in a broad sense, including probability distributions, physical extensive quantities, and Schwartz distributions of compact support. Among the particular aspects considered here are the notions of convolution, density, expectation, and conditional probability.
Keywords: monads, distributions, extensive quantities
2000 MSC: 18C15, 18D25, 46T30
Theory and Applications of Categories, Vol. 26, 2012, No. 4, pp 97-131.