Lemma 22.19.3. Let $(A, \text{d})$ be a differential graded algebra. Then we have

\[ \mathop{\mathrm{Hom}}\nolimits _{\text{Mod}_{(A, \text{d})}}(M, A^\vee [k]) = \mathop{\mathrm{Ker}}(\text{d} : (M^\vee )^ k \to (M^\vee )^{k + 1}) \]

and

\[ \mathop{\mathrm{Hom}}\nolimits _{K(\text{Mod}_{(A, \text{d})})}(M, A^\vee [k]) = H^ k(M^\vee ) \]

as functors in the differential graded $A$-module $M$.

## Comments (2)

Comment #535 by m.o. on

Comment #547 by Johan on