The Stacks project

Definition 22.7.1. Let $(A, \text{d})$ be a differential graded algebra.

1. A homomorphism $K \to L$ of differential graded $A$-modules is an admissible monomorphism if there exists a graded $A$-module map $L \to K$ which is left inverse to $K \to L$.

2. A homomorphism $L \to M$ of differential graded $A$-modules is an admissible epimorphism if there exists a graded $A$-module map $M \to L$ which is right inverse to $L \to M$.

3. A short exact sequence $0 \to K \to L \to M \to 0$ of differential graded $A$-modules is an admissible short exact sequence if it is split as a sequence of graded $A$-modules.