Graphs, hypergraphs, and properads
arXiv:1407.3744
Abstract
A categorical formalism for directed graphs is introduced, featuring natural notions of morphisms and subgraphs, and leading to two elementary descriptions of the free-properad monad, first in terms of presheaves on elementary graphs, second in terms of groupoid-enriched hypergraphs.
v2: substantial revision: corrected a few mistakes concerning convexity; added more details regarding colimits of graphs, associativity of the monad multiplication, generic factorisation, and the nerve theorem; added six references; 40 pages. v3: typos and references; submitted