ScalingStacks

Remark 5.3.12.

The statement of lemma 5.3.11 is false when \(j >n \geq k\). For example, let \(\mathcal A\) be the free \((\infty,1)\)-category generated by two objects \(a\) and \(b\), a morphism \(f\colon a\rightarrow b\) and a morphism \(g \colon b \rightarrow a.\) Then, the unique functor \(F\colon \mathcal A\rightarrow{\sf pt}\) is \(0\)-surjective, but \(\iota_0 F \colon \iota_0 \mathcal A= S^0 \rightarrow{\sf pt}\) is not \(0\)-connected.