I want to consider $L \subset A^* \times B^*$ as a "language". Is there standard terminology for this?
I wrote "double language" first (but that doesn't sound right to me), then "square language" (but languages can be squared in various ways), then "pair language" (maybe ok?), or just "language". The issue with just "language" is that it doesn't convey that there's a sort of "type hierarchy" of languages, which would be useful for me (just informally that is, don't read too much into the word "type", I barely know what it means). Eventually I figured maybe someone has already called this something and I should use the same.
My paper is in symbolic dynamics (or something like that), where I think no term is fixed for this. I am sure I have seen such "languages" in the theory of formal languages, in automata theory, and in combinatorics on words, but I can't really put my finger on any specific reference where they play a prominent role.
You can also just give your expert (or other) suggestion.