RELATIVE GRAPHS AND PULLBACKS OF RELATIVE TOEPLITZ GRAPH ALGEBRAS

We generalize a result from a recent paper of Hajac, Reznikoff and Tobolski. In that paper they give conditions they call "admissibility" on a pushout diagram in the category of directed graphs implying that the C*-algebras of the graphs form a pullback diagram. We consider a larger category of "relative graphs" that correspond to relative Toeplitz graph algebras. In this setting we give necessary and sufficient conditions on the pushout to get a pullback of C*-algebras. This is joint work with Samantha Brooker.