Yeah, category theory is a framework for describing mathematical structure. It's not vacuous -- there are mathematical structures which don't fit into the fra

Yeah, category theory is a framework for describing mathematical structure. It's not vacuous -- there are mathematical structures which don't fit into the framework and there are some theorems about what properties a category has. But category theory doesn't do that much on its own. The geometric Langlands conjectures are a _lot_ more specific, and a lot more focused. They're a big deal, because they're a toy model for the arithmetic Langlands conjectures, which are a generalization of the machinery that proved Fermat's Last Theorem and would give an effective method for dealing with a lot of number theory problems.