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Decomposition spaces, incidence algebras and Mobius inversion III: the decomposition space of Möbius intervals

Author
Galvez, M.; Kock, J.; Tonks, A.
Type of activity
Journal article
Journal
Date of publication
2018-08-20
Volume
334
First page
544
Last page
584
DOI
https://doi.org/10.1016/j.aim.2018.03.018
Project funding
GEOMETRIA DE VRIETATS I APLICACIONS (GEOMVAP)
Geomatría algebraica, simpléctica, aritmética y aplicaciones.
Geometria de varietats i aplicacions
Geometry and topology of varieties, algebra and applications
Repository
http://hdl.handle.net/2117/125325
https://arxiv.org/pdf/1512.07580
URL
https://www.sciencedirect.com/science/article/pii/S0001870818301051
Abstract
Decomposition spaces are simplicial 8-groupoids subject to a certain exactness condition, needed to induce a coalgebra structure on the space of arrows. Conservative ULF functors (CULF) between decomposition spaces induce coalgebra homomorphisms. Suitable added finiteness conditions define the notion of Möbius decomposition space, a far-reaching generalisation of the notion of Möbius category of Leroux. In this paper, we show that the Lawvere–Menni Hopf algebra of Möbius intervals, which co...
Citation
Galvez, M., Kock, J., Tonks, A. Decomposition spaces, incidence algebras and Mobius inversion III: the decomposition space of Möbius intervals. "Advances in mathematics", 20 Agost 2018, vol. 334, p. 544-584.
Keywords
2-Segal space, CULF functor, Möbius interval, Möbius inversion, decomposition space
Group of research
GEOMVAP - Geometry of Manifolds and Applications