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

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Algebra and Coalgebra in Computer Science (CALCO 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3629))

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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.

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Authors and Affiliations

  1. Computing Laboratory, Oxford University, Wolfson Building, Parks Road, Oxford, OX1 3QD, U.K

    Samson Abramsky

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  1. Samson Abramsky
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Leicester, University Road, LE1 7RH, Leicester, UK

    José Luiz Fiadeiro

  2. Department of Computer Science, University of Wales Swansea, SA2 8PP, Swansea, UK

    Neil Harman

  3. University of Wales Swansea, United Kingdom

    Markus Roggenbach

  4. CWI and Vrije Universiteit Amsterdam,  

    Jan Rutten

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Abramsky, S. (2005). Abstract Scalars, Loops, and Free Traced and Strongly Compact Closed Categories. In: Fiadeiro, J.L., Harman, N., Roggenbach, M., Rutten, J. (eds) Algebra and Coalgebra in Computer Science. CALCO 2005. Lecture Notes in Computer Science, vol 3629. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11548133_1

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  • DOI: https://doi.org/10.1007/11548133_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28620-2

  • Online ISBN: 978-3-540-31876-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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