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This work connects the idea of a "blow-up" of a quiver with that ofinjectivity, showing that for a class of monic maps $\Phi$, a quiver is$\Phi$-injective if and only if all blow-ups of it are as well. Thisrelationship is then used to characterize all quivers that are injective withrespect to the natural embedding of $P_{n}$ into $C_{n}$.

On Blow-Ups and Injectivity of Quivers