A quantale, with commutativity,
\\[
\begin{align}
x\star \left (\bigvee_{i \in I} y_i \right) = \bigvee_{i \in I}(x \star y_i) \\\\
= \bigvee_{i \in I} (y_i \star x) \\\\
= \left (\bigvee_{i \in I} y_i \right ) \star x,
\end{align}
\\]
is a lot like the higher-order function [\\(\mathrm{map}\\)](https://en.wikipedia.org/wiki/Map_(higher-order_function)),

\\[
\begin{align}
\mathrm{map}(f,\\{x_1,x_2,x_3,\cdots,x_n\\} ) \\\\
= \\{f(x_1),f(x_2),f(x_3),\cdots,f(x_n)\\}
\end{align}
\\]

except it's *nicer* in that it's commutative.