Commuting Groups and the Topos of Triads

  title={Commuting Groups and the Topos of Triads},
  author={Thomas M. Fiore and Thomas Noll},
The goal of this article is to clarify the relationship between the topos of triads and the neo-Riemannian PLR-group. To do this, we first develop some theory of generalized interval systems: 1) we prove the well known fact that every pair of dual groups is isomorphic to the left and right regular representations of some group (Cayley's Theorem), 2) given a simply transitive group action, we show how to construct the dual group, and 3) given two dual groups, we show how to easily construct sub… 

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Triads and topos theory

  • REU Project, University of Chicago
  • 2007