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 J. Kock and A. Tonks},
  journal={Advances in Mathematics},
  year={2018},
  volume={331},
  pages={952-1015}
}
  • Imma G'alvez-Carrillo, J. Kock, A. Tonks
  • Published 2018
  • Mathematics
  • Advances in Mathematics
  • Abstract This is the first in a series of papers devoted to the theory of decomposition spaces, a general framework for incidence algebras and Mobius inversion, where algebraic identities are realised by taking homotopy cardinality of equivalences of ∞-groupoids. A decomposition space is a simplicial ∞-groupoid satisfying an exactness condition, weaker than the Segal condition, expressed in terms of active and inert maps in . Just as the Segal condition expresses composition, the new exactness… CONTINUE READING
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