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.