Excisive triads and double mapping cylinders (Q1296310)

Given a topological space \(X=X_0\cup X_1\), there is a quotient map \(\pi:M\to X\), where \(M\) denotes the mapping cylinder of the cotriad \(X_0 \leftarrow X_2=X_0\cap X_1\rightarrow X_1\). In this paper, the author shows that if \((X;X_0,X_1)\) is excisive, then \(\pi\) is a weak equivalence. Using this, he obtains the correct proof of a theorem on maps of excisive triads due to J. P. May.