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

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/2117/84104
URL
http://arxiv.org/abs/1512.07580
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 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 contains th...
Citation
Galvez, M., Kock, J., Tonks, A. "Decomposition spaces, incidence algebras and Möbius inversion III: the decomposition space of Möbius intervals". 2015.
Keywords
Algebraic Topology, Combinatorics
Group of research
GEOMVAP - Geometry of Manifolds and Applications