Commutative squares as cocones

Convention 1.7.15. From now on, given a diagram \(\pushoutto C\) encoded by two morphisms \(f\colon x \to y\) and \(g\colon x \to z\), we will always use the lemma to identify cocones over this diagram with commutative squares in \(C\) of the form

Similarly, given morphisms \(h\colon y \to w\) and \(k\colon z \to w\), we will identify cones over the corresponding diagram \(\pullbackto C\) with commutative squares of the above form.