We write $a\odot x$ for the element $\webleft [\webleft (a,x\webright )\webright ]$ of

\begin{align*} A\odot X & \cong \bigvee _{a\in A}\webleft (X,x_{0}\webright )\\ & \mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}\webleft (\coprod _{i\in I}X_{i}\webright )/\mathord {\sim }.\end{align*}

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