Monads and extensive quantities

Anders Kock

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arXiv · 1103.6009

Monads and extensive quantities

Anders Kock

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Abstract

If T is a commutative monad on a cartesian closed category, then there exists a natural T-bilinear pairing from T(X) times the space of T(1)-valued functions on X ("integration"), as well as a natural T-bilinear action on T(X) by the space of these functions. These data together make the endofunctors T and "functions into T(1)" into a system of extensive/intensive quantities, in the sense of Lawvere. A natural monad map from T to a certain monad of distributions (in the sense of functional analysis (Schwartz)) arises from this integration.

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Anders Kock. 2011-03-30. Monads and extensive quantities. https://arxiv.org/abs/1103.6009

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