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Axiomatization of the coherence property for categories of symmetries. (English) Zbl 0940.18003
Ciobanu, Gabriel (ed.) et al., Fundamentals of computation theory. 12th international symposium, FCT ’99. Iaşi, Romania, August 30 - September 3, 1999. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 1684, 386-397 (1999).
Summary: Given an equational theory \((\Sigma,E)\), a relaxed \((\Sigma,E)\)-system is a category \({\mathcal S}\) enriched with a \(\Sigma\)-algebra structure on both objects and arrows such that a natural isomorphism \(\alpha_{ \mathcal S}: t_{\mathcal S} \Rightarrow t_{\mathcal S}'\), called natural symmetry, exists for each \(t=_Et'\). 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 \((\Sigma,E)\)-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.
For the entire collection see [Zbl 0921.00033].

18C10 Theories (e.g., algebraic theories), structure, and semantics
68Q42 Grammars and rewriting systems
18C50 Categorical semantics of formal languages