Article ID Journal Published Year Pages File Type
8905142 Advances in Mathematics 2017 55 Pages PDF
Abstract
We give a general categorical construction that yields several monads of measures and distributions as special cases, alongside several monads of filters. The construction takes place within a categorical setting for generalized functional analysis, called a functional-analytic context, formulated in terms of a given monad or algebraic theory T enriched in a closed category V. By employing the notion of commutant for enriched algebraic theories and monads, we define the functional distribution monad associated to a given functional-analytic context. We establish certain general classes of examples of functional-analytic contexts in cartesian closed categories V, wherein T is the theory of R-modules or R-affine spaces for a given ring or rig R in V, or the theory of R-convex spaces for a given preordered ring R in V. We prove theorems characterizing the functional distribution monads in these contexts, and on this basis we establish several specific examples of functional distribution monads.
Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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