• The Fold Map. We have a natural transformation
    called the fold map, whose component
    \[ \nabla _{X} \colon X\vee X \to X \]

    at $X$ is given by

    \[ \nabla _{X}\webleft (p\webright )\mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}\begin{cases} x & \text{if $p=\webleft [\webleft (0,x\webright )\webright ]$,}\\ x & \text{if $p=\webleft [\webleft (1,x\webright )\webright ]$} \end{cases} \]

    for each $p\in X\vee X$.


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