Decomposition spaces, incidence algebras and Möbius inversion III: the decomposition space of Möbius intervals
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 Mö...
| Autores: | , , |
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| Formato: | informe técnico |
| Fecha de publicación: | 2015 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/84104 |
| Acesso em linha: | https://hdl.handle.net/2117/84104 |
| Access Level: | acceso abierto |
| Palavra-chave: | 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 Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraica |
| Resumo: | 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 |
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