Decomposition spaces, incidence algebras and Möbius inversion I: Basic theory

@article{GalvezCarrillo2018DecompositionSI,
  title={Decomposition spaces, incidence algebras and M{\"o}bius inversion I: Basic theory},
  author={Imma G'alvez-Carrillo and Joachim Kock and Andrew Tonks},
  journal={Advances in Mathematics},
  year={2018}
}

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Decomposition spaces, incidence algebras and Möbius inversion

We introduce the notion of decomposition space as a general framework for incidence algebras and M\"obius inversion: it is a simplicial infinity-groupoid satisfying an exactness condition weaker than

Decomposition spaces in combinatorics

A decomposition space (also called unital 2-Segal space) is a simplicial object satisfying an exactness condition weaker than the Segal condition: just as the Segal condition expresses (up to

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An unpublished result by the first author states that there exists a Hopf algebra H such that for any Möbius category C (in the sense of Leroux) there exists a canonical algebra morphism from the

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