Abstract Tensor Systems as Monoidal Categories

  title={Abstract Tensor Systems as Monoidal Categories},
  author={Aleks Kissinger},
  booktitle={Categories and Types in Logic, Language, and Physics},
  • A. Kissinger
  • Published in
    Categories and Types in Logic…
    16 August 2013
  • Mathematics
The primary contribution of this paper is to give a formal, categorical treatment to Penrose’s abstract tensor notation, in the context of traced symmetric monoidal categories. To do so, we introduce a typed, sum-free version of an abstract tensor system and demonstrate the construction of its associated category. We then show that the associated category of the free abstract tensor system is in fact the free traced symmetric monoidal category on a monoidal signature. A notable consequence of… 

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