Galois connection for multiple-output operations

Emil Jeřábek

doi:10.1007/s00012-018-0499-7

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arXiv · 1612.04353

Galois connection for multiple-output operations

Emil Jeřábek

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Abstract

It is a classical result from universal algebra that the notions of polymorphisms and invariants provide a Galois connection between suitably closed classes (clones) of finitary operations $f\colon B^n\to B$, and classes (coclones) of relations $r\subseteq B^k$. We will present a generalization of this duality to classes of (multi-valued, partial) functions $f\colon B^n\to B^m$, employing invariants valued in partially ordered monoids instead of relations. In particular, our set-up encompasses the case of permutations $f\colon B^n\to B^n$, motivated by problems in reversible computing.

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Emil Jeřábek. 2017-07-29. Galois connection for multiple-output operations. https://doi.org/10.1007/s00012-018-0499-7

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