Morphisms of Generalized Interval Systems and PR-Groups

Details Morphisms of Generalized Interval Systems and PR-Groups Morphisms of Generalized Interval Systems and PR-Groups

2012-04-25

arxiv.org/abs/1204.5531v1

Mathematics

Group Theory

23 pages

Scientific paper

We begin the development of a categorical perspective on the theory of generalized interval systems (GIS's). Morphisms of GIS's allow the analyst to move between multiple interval systems and connect transformational networks. We expand the analytical reach of the Sub Dual Group Theorem of Fiore--Noll (2011) and the generalized contextual group of Fiore--Satyendra (2005) by combining them with a theory of GIS morphisms. Concrete examples include an analysis of Schoenberg, String Quartet Number 1, Opus 7, and simply transitive covers of the octatonic set. This work also lays the foundation for a transformational study of Lawvere--Tierney upgrades in the topos of triads of Noll (2005).

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