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## Decomposition spaces, incidence algebras and Möbius inversion I: basic theory

Author
Galvez, M.; Kock, J.; Tonks, A.
Type of activity
Report
Date
2015-12
Project funding
Geomatría algebraica, simpléctica, aritmética y aplicaciones.
Geometria de varietats i aplicacions
Geometry and topology of varieties, algebra and applications
Repository
http://hdl.handle.net/2117/84102
URL
http://arxiv.org/abs/1512.07573
Abstract
This is the first in a series of papers devoted to the theory of decomposition spaces, a general framework for incidence algebras and Möbius inversion, where algebraic identities are realised by taking homotopy cardinality of equivalences of 8-groupoids. A decomposition space is a simplicial 8-groupoid satisfying an exactness condition, weaker than the Segal condition, expressed in terms of generic and free maps in ¿. Just as the Segal condition expresses up-to-homotopy composition, the new co...
Citation
Galvez, M., Kock, J., Tonks, A. "Decomposition spaces, incidence algebras and Möbius inversion I: basic theory". 2015.
Keywords
Algebraic Topology, Combinatorics
Group of research
GEOMVAP - Geometry of Manifolds and Applications