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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].

##### MSC:
 18C10 Theories (e.g., algebraic theories), structure, and semantics 68Q42 Grammars and rewriting systems 18C50 Categorical semantics of formal languages
##### Keywords:
equational theory; natural symmetry; coherence
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