ScalingStacks

A.2.6 Connected categories versus weakly contractible \(\infty\)-categories[00IH]

While certain results in ordinary category theory refer to connected categories (i.e. those whose groupoid completions are connected), their \(\infty\)-categorical analogs generally instead refer to weakly contractible \(\infty\)-categories (i.e. those whose \(\infty\)-groupoid completions are contractible). For instance, the forgetful functor \(\mathcal C_{c/} \rightarrow\mathcal C\) commutes with (and detects) weakly contractible colimits.⁴⁷