Categorified Noncommutative manifolds

Details Categorified Noncommutative manifolds Categorified Noncommutative manifolds

2008-11-10

arxiv.org/abs/0811.1485v4

International Journal of Modern Physics A, 15 (2009)

Physics

Mathematical Physics

This is a 14 page excerpt of the paper "Some constructions in Category theory and Noncommutative geometry" as a contribution t

Scientific paper

We construct a noncommutative geometry with generalised `tangent bundle' from Fell bundle $C^*$-categories ($E$) beginning by replacing pair groupoid objects (points) with objects in $E$. This provides a categorification of a certain class of real spectral triples where the Dirac operator is constructed from morphisms in a category. Applications for physics include quantisation via the tangent groupoid and new constraints on $D_{\mathrm{finite}}$ (the fermion mass matrix).

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