Axiomatization of the Coherence Property for Categories of Symmetries

Authors:
Dorel Lucanu
Affiliations:
-
Venue:
FCT '99 Proceedings of the 12th International Symposium on Fundamentals of Computation Theory
Year:
1999

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Abstract

Given an equational theory (Σ,E), a relaxed (Σ,E)-system is a category S enriched with a Σ-algebra structure on both objects and arrows such that a natural isomorphism αS : tS ⇒ t′S, called natural symmetry, exists for each t =E t′. A symmetry is an instance of a natural symmetry. A category of symmetries, which includes only symmetries, is a free object in the category of relaxed (Σ,E)-systems. The coherence property states that the diagrams in a category of symmetries are commutative. In this paper we present a method for expressing the coherence property in an axiomatic way.