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Levi categories and graphs of groups

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Mark V. Lawson and Alistair R. Wallis

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.

Keywords:
Graphs of groups, self-similar groupoid actions, cancellative categories

2010 MSC:
18B40, 20E06

*Theory and Applications of Categories,*
Vol. 32, 2017,
No. 23, pp 780-802.

Published 2017-07-27.

http://www.tac.mta.ca/tac/volumes/32/23/32-23.pdf

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