The Cocone. The maps
\begin{align*} \mathrm{inj}_{1} & \colon A \to A\mathchoice {\mathbin {\textstyle \coprod }}{\mathbin {\textstyle \coprod }}{\mathbin {\scriptstyle \textstyle \coprod }}{\mathbin {\scriptscriptstyle \textstyle \coprod }}B,\\ \mathrm{inj}_{2} & \colon B \to A\mathchoice {\mathbin {\textstyle \coprod }}{\mathbin {\textstyle \coprod }}{\mathbin {\scriptstyle \textstyle \coprod }}{\mathbin {\scriptscriptstyle \textstyle \coprod }}B, \end{align*}
given by
\begin{align*} \mathrm{inj}_{1}\webleft (a\webright ) & \mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}\webleft (0,a\webright ),\\ \mathrm{inj}_{2}\webleft (b\webright ) & \mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}\webleft (1,b\webright ), \end{align*}
for each $a\in A$ and each $b\in B$.