Finite dimensional vector spaces are complete for traced symmetric monoidal categories

Authors:
Masahito Hasegawa;Martin Hofmann;Gordon Plotkin
Affiliations:
RIMS, Kyoto University;LMU München, Institut für Informatik;LFCS, University of Edinburgh
Venue:
Pillars of computer science
Year:
2008

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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.