The functoriality of moves on graphs and the extended covariant functoriality of graph algebras (opens in new tab)

Combinatorics of graphs is a very powerful tool to unravel various properties of graph algebras. In particular, isomorphisms between graph algebras are often implemented by moves between their graphs. In this paper, we make these combinatorial methods functorial, and show that collapsing an out-split graph to the original graph and transforming a graph to a shifted graph can be implemented by admissible graph homomorphisms and admissible path ...