Shape of sheaf topos

Let \(X\) be a paracompact, locally contractible topological space. Then \(\Shv(X)\) is essential and its shape is represented by the singular anima \(\Pi_\infty X\). Without a local contractibility hypothesis, the shape need not be represented by the weak homotopy type of \(X\); the pro-object can retain information which the singular anima loses. See [Lurie 2017, Appendix A].