An "almost" full embedding of the category of graphs into the category of groups

Details An "almost" full embedding of the category of graphs into the category of groups An "almost" full embedding of the category of graphs into the category of groups

2009-12-02

arxiv.org/abs/0912.0510v2

Mathematics

Group Theory

24 pages; to appear in Adv. Math.

Scientific paper

10.1016/j.aim.2010.04.015

We construct a functor from the category of graphs to the category of groups which is faithful and "almost" full, in the sense that it induces bijections of the Hom sets up to trivial homomorphisms and conjugation in the category of groups. We provide several applications of this construction to localizations (i.e. idempotent functors) in the category of groups and the homotopy category.

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