Lemma 22.12.1. Let $(A, \text{d})$ be a differential graded algebra. Let $I \to M$ be an injective homomorphism of differential graded $A$-modules. If $I$ is an injective object of the category of graded $A$-modules, then $I \to M$ is an admissible monomorphism.

**Proof.**
This is immediate from the definitions.
$\square$

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