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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)

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 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.

Keywords

Commutative Diagram Natural Transformation Natural Isomorphism Monoidal Category Coherent System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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