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This work connects the idea of a "blow-up" of a quiver with that of injectivity, showing that for a class of monic maps Φ, a quiver is Φ-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 .the electronic journal of combinatorics 16 (2009), #R00 Sections and Retractions in QuivRecall from [1, Definition 7.19] that a section in a category is a morphism that is leftinvertible. Also, [1, Definition 7.24] gives the dual notion of a section as a retraction, a the electronic journal of combinatorics 16 (2009), #R00

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