Commutative monads as a theory of distributions

Anders Kock

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.

Published 2012-02-24.

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