Cellular cohomology in homotopy type theory

Ulrik Buchholtz, Kuen Bang Hou Favonia

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

We present a development of cellular cohomology in homotopy type theory. Cohomology associates to each space a sequence of abelian groups capturing part of its structure, and has the advantage over homotopy groups in that these abelian groups of many common spaces are easier to compute. Cellular cohomology is a special kind of cohomology designed for cell complexes: these are built in stages by attaching spheres of progressively higher dimension, and cellular cohomology defines the groups out of the combinatorial description of how spheres are attached. Our main result is that for finite cell complexes, a wide class of cohomology theories (including the ones defined through Eilenberg-MacLane spaces) can be calculated via cellular cohomology. This result was formalized in the Agda proof assistant.

Original languageEnglish (US)
Title of host publicationProceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages521-529
Number of pages9
ISBN (Electronic)9781450355834, 9781450355834
DOIs
StatePublished - Jul 9 2018
Externally publishedYes
Event33rd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2018 - Oxford, United Kingdom
Duration: Jul 9 2018Jul 12 2018

Publication series

NameProceedings - Symposium on Logic in Computer Science
ISSN (Print)1043-6871

Conference

Conference33rd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2018
CountryUnited Kingdom
CityOxford
Period7/9/187/12/18

Keywords

  • Cellular cohomology
  • Homotopy type theory
  • Mechanized reasoning

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  • Cite this

    Buchholtz, U., & Favonia, K. B. H. (2018). Cellular cohomology in homotopy type theory. In Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2018 (pp. 521-529). (Proceedings - Symposium on Logic in Computer Science). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1145/3209108.3209188