Abstract
This paper introduces and studies a categorical analogue of the familiar monoid semiring construction. By introducing an axiomatisation of summation that unifies notions of summation from algebraic program semantics with various notions of summation from the theory of analysis, we demonstrate that the monoid semiring construction generalises to cases where both the monoid and the semiring are categories. This construction has many interesting and natural categorical properties, and natural computational interpretations.
Publisher
Cambridge University Press (CUP)
Subject
Computer Science Applications,Mathematics (miscellaneous)
Reference31 articles.
1. Abstrakte Funktionen und lineare Operatoren;Gelfand;Recueil Math'ematique [Mat. Sbornik] N.S.,1938
2. Subseries in Banach spaces.;Lahiri;Mathematica Slovaca,2002
3. Power Algebras over Semirings
4. Tensor product of partially-additive monoids
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