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Decomposition spaces, incidence algebras and Möbius inversion

Author
Galvez, M.; Kock, J.; Tonks, A.
Type of activity
Report
Date
2014-04-11
Project funding
Geomatría algebraica, simpléctica, aritmética y aplicaciones.
Repository
http://hdl.handle.net/2117/23130 Open in new window
URL
http://arxiv.org/abs/1404.3202 Open in new window
Abstract
We introduce the notion of decomposition space as a general framework for incidence algebras and M\"obius inversion: it is a simplicial infinity-groupoid satisfying an exactness condition weaker than the Segal condition, which expresses decomposition. We work on the objective level of homotopy linear algebra with coefficients in infinity-groupoids, developed along the way. To any (complete) decomposition space there is associated an incidence (co)algebra (with coefficients in infinity-groupoids)...
Citation
Galvez, M.; Kock, J.; Tonks, A. "Decomposition spaces, incidence algebras and Möbius inversion". 2014.
Keywords
Algebraic topology, Combinatorics
Group of research
GEOMVAP - Geometry of Manifolds and Applications

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