Commutative monads as a theory of distributions

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Abstract

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.
Original languageEnglish
JournalTheory and Applications of Categories
Volume26
Issue4
Pages (from-to)97-131
Number of pages35
ISSN1201-561X
Publication statusPublished - 2012

Keywords

  • monads
  • distributions
  • extensive quantities

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