• The Cocone.The collection
    \[ \webleft\{ \mathrm{inj}_{\gamma }\colon X_{\gamma }\to \operatorname*{{\displaystyle \underset {\longrightarrow }{\operatorname*{\text{colim}}}}}_{\alpha \in I}\webleft (X_{\alpha }\webright )\webright\} _{\gamma \in I} \]

    of maps of sets defined by

    \[ \mathrm{inj}_{\gamma }\webleft (x\webright )\mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}\webleft [\webleft (\gamma ,x\webright )\webright ] \]

    for each $\gamma \in I$ and each $x\in X_{\gamma }$.


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