Definition 1.7.11. Let \(C\) be an \(\infty \)-category, and let \(f\colon x \to y\) and \(g\colon x \to z\) be two morphisms in \(C\), corresponding to a functor \(\pushoutto C\). We refer to a colimit of this functor as a pushout of \(y\) and \(z\) along \(x\). We will denote a pushout by \(y \sqcup _x z\), if it exists.
Dually, given morphisms \(h\colon y \to w\) and \(k\colon z \to w\), we refer to a limit of the corresponding functor \(\pullbackto C\) as a pullback of \(y\) and \(z\) over \(w\), and denote it by \(y \times _w z\).
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