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

Author
Galvez, M.; Kock, J.; Tonks, A.
Type of activity
Journal article
Journal
Date of publication
2018-06-20
Volume
331
First page
952
Last page
1015
DOI
https://doi.org/10.1016/j.aim.2018.03.016
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/2117/125233
URL
https://www.sciencedirect.com/science/article/pii/S0001870818301038
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 active and inert maps in Image 1. Just as the Segal condition expresses composition, the new exactness co...
Citation
Galvez, M., Kock, J., Tonks, A. Decomposition spaces, incidence algebras and Möbius inversion I: basic theory. "Advances in mathematics", 20 Juny 2018, vol. 331, p. 952-1015.
Keywords
2-Segal space, CULF functor, Hall algebra, Segal space, decomposition space, incidence algebra
Group of research
GEOMVAP - Geometry of Manifolds and Applications