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Commutative monads as a theory of distributions
Theory and applications of categories, Tome 26 (2012), pp. 97-131 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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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.

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Classification : 18C15, 18D25, 46T30
Keywords: monads, distributions, extensive quantities 
@article{TAC_2012_26_a3,
     author = {Anders Kock},
     title = {Commutative monads as a theory of distributions},
     journal = {Theory and applications of categories},
     pages = {97--131},
     year = {2012},
     volume = {26},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2012_26_a3/}
}
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Anders Kock. Commutative monads as a theory of distributions. Theory and applications of categories, Tome 26 (2012), pp. 97-131. http://geodesic.mathdoc.fr/item/TAC_2012_26_a3/