Abstract
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 language | English |
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Pages (from-to) | 780-802 |
Number of pages | 23 |
Journal | Theory and Applications of Categories |
Volume | 32 |
Issue number | 23 |
Early online date | 27 Jul 2017 |
Publication status | E-pub ahead of print - 27 Jul 2017 |
Keywords
- Graphs of groups
- self-similar groupoid actions
- cancellative categories
ASJC Scopus subject areas
- Mathematics(all)
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Mark Lawson
- School of Mathematical & Computer Sciences - Professor
- School of Mathematical & Computer Sciences, Mathematics - Professor
Person: Academic (Research & Teaching)