Calculating Colimits Compositionally
R. Rosebrugh, N. Sabadini, R.F.C. Walters
TL;DR
This paper demonstrates a method to compute finite limits and colimits in a compositional manner using span and cospan algebras, with an application to proving the Kleene Theorem on regular languages.
Contribution
It introduces a novel compositional approach to calculating limits and colimits via span and cospan algebras, providing a new proof of Kleene's Theorem.
Findings
Finite limits and colimits can be computed compositionally.
Span and cospan algebras are effective tools for such calculations.
A new proof of Kleene's Theorem on regular languages is provided.
Abstract
We show how finite limits and colimits can be calculated compositionally using the algebras of spans and cospans, and give as an application a proof of the Kleene Theorem on regular languages.
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Taxonomy
TopicsAdvanced Algebra and Logic · semigroups and automata theory · Logic, programming, and type systems