Algebra universalis

, 79:17 | Cite as

Galois connection for multiple-output operations

  • Emil Jeřábek


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 \(f:B^n\rightarrow B\), and classes (coclones) of relations \(r\subseteq B^k\). We will present a generalization of this duality to classes of (multi-valued, partial) functions \(f:B^n\rightarrow B^m\), employing invariants valued in partially ordered monoids instead of relations. In particular, our set-up encompasses the case of permutations \(f:B^n\rightarrow B^n\), motivated by problems in reversible computing.


Clones and coclones Galois connection Multiple-output operations Partially ordered monoids 

Mathematics Subject Classification

08A40 06F05 06A15 


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Mathematics of the Czech Academy of SciencesPraha 1Czech Republic

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