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Decomposition spaces, incidence algebras and Mobius inversion II: Completeness, length filtration, and finiteness

Author
Galvez, M.; Kock, J.; Tonks, A.
Type of activity
Journal article
Journal
Advances in mathematics
Date of publication
2018-07-31
Volume
333
First page
1242
Last page
1292
DOI
https://doi.org/10.1016/j.aim.2018.03.017 Open in new window
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/2117/125234 Open in new window
URL
https://www.sciencedirect.com/science/article/pii/S000187081830104X?via%3Dihub Open in new window
Abstract
This is the second in a trilogy of papers introducing and studying the notion of decomposition space as a general framework for incidence algebras and Möbius inversion, with coefficients in 8-groupoids. A decomposition space is a simplicial 8-groupoid satisfying an exactness condition weaker than the Segal condition. Just as the Segal condition expresses composition, the new condition expresses decomposition. In this paper, we introduce various technical conditions on decomposition spaces. The...
Citation
Galvez, M., Kock, J., Tonks, A. Decomposition spaces, incidence algebras and Mobius inversion II: Completeness, length filtration, and finiteness. "Advances in mathematics", 31 Juliol 2018, vol. 333, p. 1242-1292.
Keywords
2-Segal space, Mobius inversion, decomposition space, homotopy cardinality, incidence algebra, length filtration
Group of research
GEOMVAP - Geometry of Manifolds and Applications

Participants