Every language L is spoken/cognized by some one or more speakers.That is, the claim that languages can be reduced to cognitve states of some one or more speakers. However, I think that cognitive reductionism is deeply mistaken. There are languages which are not spoken, or cognized.
So, on my view, statements of the form:
Agent A cognizes language Lare contingent empirical claims. The agent A might not have cognized L. Whether agents A and B cognize a "shared" language is an empirical question.
Agents A and B cognize the same ("shared") language L.
It seems clear that, as a matter of empirical observation, agents never cognize the same language (though this is contingent, of course). There are lexical, phonological, semantic, pragmatic, etc., differences. And this phenomenon---heterogeneity in speech communities---requires explanation.