2011/06/06 by Will Grilliette, Grilliette, Will
Mathematics · #18B05 #Category Theory (math.CT) #Combinatorics (math.CO) #FOS: Mathematics #math.CO #math.CT #msc:18B05
paper · pdf · doi:10.48550/arxiv.1106.1063
10 pages This paper has been withdrawn as it was subsumed by arXiv:1608.00058
arxiv created 2017/06/03 · arxiv updated 2017/06/06
In this paper, I characterize four particular classes of directed multigraphs, or quivers, as images under left and right adjoints to the natural vertex and edge functors. In particular, the following notions coincide: (1) independent sets of vertices with a left adjoint functor to the vertex functor, (2) independent sets of edges with a left adjoint functor to the edge functor, (3) complete digraphs with a right adjoint functor to the vertex functor, (4) bouquets with a right adjoint functor to the edge functor.