Decomposition spaces, incidence algebras and Mobius 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 (CULF) between decomposition spaces induce coalgebra homomorphisms. Suitable added finiteness conditions define the notio...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/125325 |
| Acceso en línea: | https://hdl.handle.net/2117/125325 https://dx.doi.org/10.1016/j.aim.2018.03.018 |
| Access Level: | acceso abierto |
| Palabra clave: | Algebraic topology Combinatorial topology decomposition space 2-Segal space CULF functor Möbius interval Möbius inversion 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 |
| Sumario: | 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 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 for Möbius decomposition spaces and CULF functors. |
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