Axiomatization of the coherence property for categories of symmetries

  • Dorel Lucanu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1684)


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 σ StS), 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.


Commutative Diagram Natural Transformation Natural Isomorphism Monoidal Category Coherent System 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Dorel Lucanu
    • 1
  1. 1.Faculty of Computer Science“A.I. Cuza” UniversityIaşiRomania

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