is there a name for the class of functions $f: L\times L \rightarrow L$, where $L$ is a lattice and $L\times L$ is the product lattice (ordered pointwise), with the following property:
$f(x,y)=f( x \vee y, x \wedge y)$ ?
The symbols $\vee$ and $\wedge$ denote the binary join and meet operations on lattices.
thank you in advance.