Levi categories and graphs of groups

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2 Citations (Scopus)


We define a Levi category to be a weakly orthogonal category equipped with a suitable length functor and prove two main theorems about them. First, skeletal cancellative Levi categories are precisely the categorical versions of graphs of groups with a given orientation. Second, the universal groupoid of a skeletal cancellative Levi category is the fundamental groupoid of the corresponding graph of groups. These two results can be viewed as a co-ordinate-free refinement of a classical theorem of Philip Higgins.
Original languageEnglish
Pages (from-to)780-802
Number of pages23
JournalTheory and Applications of Categories
Issue number23
Early online date27 Jul 2017
Publication statusE-pub ahead of print - 27 Jul 2017


  • Graphs of groups
  • self-similar groupoid actions
  • cancellative categories

ASJC Scopus subject areas

  • General Mathematics


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