Universal Associative Geometry

2014/06/06 by Wolfgang Bertram, Bertram, Wolfgang
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Category Theory (math.CT) #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1406.1692

openalex publication_date 2014/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We generalize parts of the theory of associative geometries developed by Kinyon and the author in the framework of universal algebra: we prove that certain associoid structures, such as pregroupoids and principal equivalence relations, have a natural prolongation from a set to its the power set. We reinvestigate the case of homogeneous pregroupoids (corresponding to the projective geometry of a group) from the point of view of pairs of commuting principal equivalence relations. We use the ternary approach to groupoids developed by Anders Kock, and the torsors defined by our construction can be seen as a generalisation of the known groups of bisections of a groupoid.

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