ScalingStacks

Proof. Since $\mathcal{C}$ is presentable and the tensor product commutes with colimits separately in each variable, for each object $X\in\mathcal{C}$ the functor $Y\mapsto X\otimes Y$ is a left adjoint and therefore preserves $n$-connected morphisms by 4.1.4. Hence, given two $n$-connected morphisms $f\colon A_{1}\to B_{1}$ and $g\colon A_{2}\to B_{2}$, the composition

$$A_{1}\otimes B_{1}\xrightarrow{A_{1}\otimes g}A_{1}\otimes B_{2}\xrightarrow{f\otimes B_{2}}A_{2}\otimes B_{2}$$

is $n$-connected as a composition of two $n$-connected morphisms. ∎