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Symmetry and its Formalisms: Mathematical aspects

Guay, Alexandre and Hepburn, Brian (2008) Symmetry and its Formalisms: Mathematical aspects. [Preprint]


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This paper explores the relation between the concept of symmetry and its formalisms. The standard view among philosophers and physicists is that symmetry is completely formalized by mathematical groups. For some mathematicians however, the groupoid is a competing and more general formalism. An analysis of symmetry which justifies this extension has not been adequately spelled out. After a brief explication of how groups, equivalence, and symmetries classes are related, we show that, while it's true in some instances that groups are too restrictive, there are other instances for which the standard extension to groupoids is too unrestrictive. The connection between groups and equivalence classes, when generalized to groupoids, suggests a middle ground between the two.

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Item Type: Preprint
Guay, Alexandre
Hepburn, Brian
Additional Information: Accepted for publication in Philosophy of Science.
Subjects: Specific Sciences > Mathematics
Depositing User: Alexandre Guay
Date Deposited: 24 Oct 2008
Last Modified: 07 Oct 2010 15:17
Item ID: 4249
Subjects: Specific Sciences > Mathematics
Date: October 2008

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