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A Role for Categories in the Foundations of Quantum Theory

Published online by Cambridge University Press:  28 February 2022

David Geoffrey Holdsworth
David Geoffrey Holdsworth*
Affiliation:
Institut für Theoretische Physik, Universität zu Köln Department of Philosophy, The University of Western Ontario
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Extract

In this paper I shall outline a possibility for incorporating category theory in an essential way into the foundations of quantum theory. The role for category theory which I shall sketch here is strictly foundational in the sense that it offers no new perspectives for a physicist working within the quantum formalism, but rather provides a way of interpreting the algebraic structure by giving an alternative axiomatization of the underlying logic of the theory. The axiomatization is given without recourse to any classical set theory by invoking methods closely connected with the work of F. W. Lawvere. More precisely, then, a possible approach to the foundations of physics which axiomatizes its algebraic structure in a way which is independent of set theory and hence points, as it were, to a structuralist foundation of physical theories, will be proposed.

Type
Part VII. Quantum Logic
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1978 , Issue 1: Volume One: Contributed Papers 1978 , 1978 , pp. 257 - 267
Copyright
Copyright © 1978 by the Philosophy of Science Association

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Footnotes

1

Work done while supported by the Heinrich Hertz Stiftung, W. Germany.

References

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