Exercise 1.5.21. Let \(l\colon C \to C[W^{-1}]\) be a localization of \(C\) at a collection of morphisms \(W \hookrightarrow \Map ([1],C)\). Show that \(l\) can be computed by the following pushout square of \(\infty \)-categories:

Commutative diagram generated from the LaTeX source

Hint: Show that if \(i\) is a full subcategory inclusion, then so is \(\Fun (W,i)\), and then use Chapterexercise 1.10, Chapterexercise 1.8.

Generated from the authoritative LaTeX source.