On Blow-Ups and Injectivity of Quivers

This work connects the idea of a “blow-up” of a quiver with that of injectivity, showing that for a class of monic maps $\mathrm{\Phi }$, a quiver is $\mathrm{\Phi }$-injective if and only if all blow-ups of it are as well. This relationship is then used to characterize all quivers that are injective with respect to the natural embedding of $P_n$ into $C_n$.