Corollary 3.45.
For \(n \geq 0\) there are equivalences
\[\mathrm{EM}_0(T) \simeq (T_{\leq 0})_*, \qquad \mathrm{EM}_1(T) \simeq \Grp(T_{\leq 0}), \quad \qquadtext{and} \quad \mathrm{EM}_n(T) \simeq \Ab(T_{\leq 0}) \quad \textup{ for $n \geq 2$.}\]
Proof
By Corollary 3.34, the equivalence \(\bOmega^n\colon T^{\geq n}_* \iso E_n\Grp(T)\) from Proposition 3.44 restricts to an equivalence
\[\bOmega^n\colon \mathrm{EM}_n(T) \iso E_n\Grp(T_{\leq 0})\]
for all \(n\), with inverse given by \(\bB^n\). But since \(T_{\leq 0}\) is a 1-category, we have \(E_n\Grp(T_{\leq 0}) \simeq \Ab(T_{\leq 0})\) for all \(n \geq 2\).