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)


We show that the category FinVect k 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 FinVect k which distinguishes them. Therefore two arrows in the free traced category are the same if and only if they agree for all interpretations in FinVect k .


Function Symbol Monoidal Category Parallel Composition Closed Network Monoidal Structure 
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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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