Commutative monads as a theory of distributions

Abstract

The theory of commutative monads on cartesian closed categories provides a framework where aspects of the theory of distributions and other extensive quantities can be formulated and some results proved. We make explicit a link between our theory and the theory of Schwartz distributions of compact support. We also discuss probability distributions.

This submission subsumes and simplifies most of two previous submissions by the author, arXiv 1103.6009 and 1105.3405