Loop group

Definition 5.1.11 (Loop group). Let \(C\) be an \(\infty \)-category with finite limits. We define the loop group \(\bOmega (X,x) \in \Fun (\simp \catop ,C)\) of a pointed object \((X,x)\) in \(C\) as the Čech nerve of the morphism \(x\colon * \to X\). This results in a functor \(\bOmega \colon C_* \to \Fun (\simp \catop ,C)\).