No, you can’t. The vast majority of analysis cannot usefully be represented in category theory. You can’t express everything in analysis using morphisms and map

No, you can’t. The vast majority of analysis cannot usefully be represented in category theory. You can’t express everything in analysis using morphisms and maps. When you’re working with structures (algebra, geometry, topology, etc), sure, you can construct them in the language of categories. But that’s very far from “all of math”.