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Abstract Scalars, Loops, and Free Traced and Strongly Compact Closed Categories

  • Samson Abramsky
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3629)

Abstract

We study structures which have arisen in recent work by the present author and Bob Coecke on a categorical axiomatics for Quantum Mechanics; in particular, the notion of strongly compact closed category. We explain how these structures support a notion of scalar which allows quantitative aspects of physical theory to be expressed, and how the notion of strong compact closure emerges as a significant refinement of the more classical notion of compact closed category.

We then proceed to an extended discussion of free constructions for a sequence of progressively more complex kinds of structured category, culminating in the strongly compact closed case. The simple geometric and combinatorial ideas underlying these constructions are emphasized. We also discuss variations where a prescribed monoid of scalars can be ‘glued in’ to the free construction.

Keywords

Tensor Product Monoidal Category Monoidal Structure Algebraic Description Symmetric Monoidal Category 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Samson Abramsky
    • 1
  1. 1.Computing LaboratoryOxford UniversityOxfordU.K

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