Definition 3.52.
Let \(A\) be an abelian group object in \(T_{\leq 0}\), and let \(Y \in T\). We define the \(n\)-th cohomology of \(Y\) with coefficients in \(A\) as
\[H^n(Y,A) := \pi_0\,\Hom_T(Y,\bB^n A) \in \Ab .\]
Definition 3.52.
Let \(A\) be an abelian group object in \(T_{\leq 0}\), and let \(Y \in T\). We define the \(n\)-th cohomology of \(Y\) with coefficients in \(A\) as