Finite Dimensional Vector Spaces Are Complete for Traced Symmetric Monoidal Categories

  • Masahito Hasegawa
  • Martin Hofmann
  • Gordon Plotkin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4800)

Abstract

We show that the category FinVectk of finite dimensional vector spaces and linear maps over any field k is (collectively) complete for the traced symmetric monoidal category freely generated from a signature, provided that the field has characteristic 0; this means that for any two different arrows in the free traced category there always exists a strong traced functor into FinVectk which distinguishes them. Therefore two arrows in the free traced category are the same if and only if they agree for all interpretations in FinVectk.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Masahito Hasegawa
    • 1
  • Martin Hofmann
    • 2
  • Gordon Plotkin
    • 3
  1. 1.RIMSKyoto University 
  2. 2.Institut für InformatikLMU München 
  3. 3.LFCSUniversity of Edinburgh 

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