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We give properties of the structural maps of monic representations, and prove that the category ${\\rm mon}(Q, I, A)$ of the monic representations of $(Q, I)$ over $A$ is a resolving subcategory of ${\\rm rep}(Q, I, A)$. We introduce the condition ${\\rm(G)}$. The main result claims that a $\\m$-module is Gorenstein-projective if and only if it is a monic module satisfying ${\\rm(G)}$. 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