Proposition 2.35. (Delooping principle)
Let \(T\) be a topos. Then there is an equivalence of categories
\[\bB \colon \Grp(T) \quad\rightleftarrows \quad T^{\geq 1}_* \noloc \bOmega.\]
Proof
The equivalence \(\Grpd(T) \simeq \mathrm{EffEpi}(T)\) from Lemma 2.33 sits in a commutative triangle 