Graphs, hypergraphs, and properads
Quantum Algebra
2016-10-04 v3 Category Theory
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.
Cite
@article{arxiv.1407.3744,
title = {Graphs, hypergraphs, and properads},
author = {Joachim Kock},
journal= {arXiv preprint arXiv:1407.3744},
year = {2016}
}
Comments
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