Título:
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Decomposition spaces, incidence algebras and Möbius inversion III: the decomposition space of Möbius intervals
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Autor/a:
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Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew
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Otros autores:
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Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. GEOMVAP - Geometria de Varietats i Aplicacions |
Abstract:
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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 the universal Möbius function (but is not induced by a Möbius category), can be realised as the homotopy cardinality of a Möbius decomposition space U of all Möbius intervals, and that in a certain sense U is universal |
Materia(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraica -Algebraic topology -Combinatorial topology -Algebraic Topology -Combinatorics -Topologia algebraica -Topologia combinatòria -Classificació AMS::18 Category theory; homological algebra::18G Homological algebra -Classificació AMS::06 Order, lattices, ordered algebraic structures::06A Ordered sets -Classificació AMS::55 Algebraic topology::55P Homotopy theory |
Derechos:
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Tipo de documento:
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Artículo - Borrador Informe |
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