Nominal lawvere theories

Authors:
Ranald Clouston
Affiliations:
Logic and Computation Group, Research School of Computer Science, The Australian National University, Canberra, Australia
Venue:
WoLLIC'11 Proceedings of the 18th international conference on Logic, language, information and computation
Year:
2011

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Abstract

Lawvere theories provide a category theoretic view of equational logic, identifying equational theories with small categories equipped with finite products. This formulation allows equational theories to be investigated as first class mathematical entities. However, many formal systems, particularly in computer science, are described by equations modulated by side conditions asserting the "freshness of names"; these may be expressed as theories of Nominal Equational Logic (NEL). This paper develops a correspondence between NEL-theories and certain categories that we call nominal Lawvere theories.