Hall (, 2)-Categories

  • Tobias Dyckerhoff
  • Mikhail Kapranov
Part of the Lecture Notes in Mathematics book series (LNM, volume 2244)


Let Open image in new window be a unital 2-Segal topological space with weakly contractible space of 0-simplices. Replacing X by a weakly equivalent simplicial space, we may assume that X is Reedy fibrant and satisfies \(X_0 = \operatorname {pt} \nolimits \). For example, the Waldhausen S-construction of an exact -category as defined in §  7.3 can be replaced by a weakly equivalent simplicial space satisfying these assumptions.


  1. [Lur07]
    Lurie, J.: Derived algebraic geometry II: noncommutative algebra. ArXiv Mathematics e-prints (2007)Google Scholar
  2. [Lur09a]
    Lurie, J.: Higher Topos Theory. Annals of Mathematics Studies, vol. 170. Princeton University Press, Princeton (2009)Google Scholar
  3. [Lur09b]
    Lurie, J.: (Infinity,2)-categories and the goodwillie calculus I. ArXiv e-prints (2009)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Tobias Dyckerhoff
    • 1
  • Mikhail Kapranov
    • 2
  1. 1.Department of MathematicsUniversity of HamburgHamburgGermany
  2. 2.Kavli Institute for the Physics and Mathematics of the UniverseKashiwaJapan

Personalised recommendations