Abstract
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 .
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Hasegawa, M., Hofmann, M., Plotkin, G. (2008). Finite Dimensional Vector Spaces Are Complete for Traced Symmetric Monoidal Categories. In: Avron, A., Dershowitz, N., Rabinovich, A. (eds) Pillars of Computer Science. Lecture Notes in Computer Science, vol 4800. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78127-1_20
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DOI: https://doi.org/10.1007/978-3-540-78127-1_20
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