Finite Dimensional Vector Spaces Are Complete for Traced Symmetric Monoidal Categories

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.

• Type: Conference
• Year: 2008
• Where: BIRTHDAY
• Authors: Masahito Hasegawa, Martin Hofmann, Gordon D. Plotkin
• Keywords: Applied Computing, BIRTHDAY 2008, Free Traced Category, Strong Traced Functor, Symmetric Monoidal Category