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Non-commutative geometry, categories and quantum physics. (English) Zbl 1157.46044
Proceedings of the international conference on mathematics and its applications, ICMA-MU 2007, Bangkok, Thailand, August 15–17, 2007. Bangkok: Mahidol University. 135-178 (2007).
The article gives a quite nice and up-to-date overview of noncommutative geometry, covering different approaches to the subject, including an outline of the authors’ own categorical approach. The last section has some discussion on the possible connections with and applications to physics, such as quantum gravity. The bibliograpghy at the end of the paper is quite exhaustive and will be valuable to any researcher in the field.
For the entire collection see [Zbl 1123.00005].

46L87 Noncommutative differential geometry
46M15 Categories, functors in functional analysis
16D90 Module categories in associative algebras
18F99 Categories in geometry and topology
81R60 Noncommutative geometry in quantum theory