Construction 5.26. (Zigzag construction, Wärn (2025))
Starting with a span \(Q_0 \leftarrow P_0 \to R_0\) over \(B \leftarrow A \to C\), define a sequence of spans
\[Q_n \leftarrow P_n \to R_n\]
by alternately making the left and right legs cartesian: for odd \(n\) we apply the left construction to the previous span, and for even \(n \geq 2\) we apply the right construction. Let
\[Q_{\infty} := \colim_n Q_n, \qquad P_{\infty} := \colim_n P_n, \qquad R_{\infty} := \colim_n R_n .\]
References
- David Wärn. Path spaces of pushouts. 2025.