Geodesic
Levi categories and graphs of groups
Theory and applications of categories, Tome 32 (2017), pp. 780-802

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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.

Publié le :
Classification : 18B40, 20E06
Keywords: Graphs of groups, self-similar groupoid actions, cancellative categories 
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     author = {Mark V. Lawson and Alistair R. Wallis},
     title = {Levi categories and graphs of groups},
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     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2017_32_a22/}
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Mark V. Lawson; Alistair R. Wallis. Levi categories and graphs of groups. Theory and applications of categories, Tome 32 (2017), pp. 780-802. http://geodesic.mathdoc.fr/item/TAC_2017_32_a22/