A categorical analogue of the monoid semiring construction
Category Theory
2013-06-03 v1 Rings and Algebras
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.
Keywords
Cite
@article{arxiv.1305.7414,
title = {A categorical analogue of the monoid semiring construction},
author = {Peter Hines},
journal= {arXiv preprint arXiv:1305.7414},
year = {2013}
}
Comments
34 pages, 5 diagrams