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On universal algebra over nominal sets

Published online by Cambridge University Press:  25 March 2010

ALEXANDER KURZ  and
DANIELA PETRIŞAN
ALEXANDER KURZ
Affiliation:
Department of Computer Science, University of Leicester, UK Email: [email protected]; [email protected]
DANIELA PETRIŞAN
Affiliation:
Department of Computer Science, University of Leicester, UK Email: [email protected]; [email protected]
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Abstract

We investigate universal algebra over the category Nom of nominal sets. Using the fact that Nom is a full reflective subcategory of a monadic category, we obtain an HSP-like theorem for algebras over nominal sets. We isolate a ‘uniform’ fragment of our equational logic, which corresponds to the nominal logics present in the literature. We give semantically invariant translations of theories for nominal algebra and NEL into ‘uniform’ theories, and systematically prove HSP theorems for models of these theories.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 20 , Special Issue 2: Domains , April 2010 , pp. 285 - 318
Copyright
Copyright © Cambridge University Press 2010

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