Decomposition spaces, incidence algebras and Mobius inversion III: The decomposition space of Mobius intervals
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Decomposition spaces are simplicial infinity-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 Mobius decomposition space, a far-reaching generalisation of the notion of Mobius category of Leroux. In this paper, we show that the Lawvere-Menni Hopf algebra of Mobius intervals, which contains the universal Mobius function (but is not induced by a Mobius category), can be realised as the homotopy cardinality of a Mobius decomposition space U of all Mobius intervals, and that in a certain sense U is universal for Mobius decomposition spaces and CULF functors. (C) 2018 Elsevier Inc. All rights reserved.
Original language | English |
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Journal | Advances in Mathematics |
Volume | 334 |
Pages (from-to) | 544-584 |
Number of pages | 41 |
ISSN | 0001-8708 |
DOIs | |
Publication status | Published - 20 Aug 2018 |
Externally published | Yes |
- decomposition space, 2-Segal space, GULF functor, Mobius interval, Mobius inversion, CATEGORIES
Research areas
ID: 331498039