> that illustates that we need this apparatus to solve some real problem? I think your question is wrong in a sense. Category theory is one of several languagu

> that illustates that we need this apparatus to solve some real problem? I think your question is wrong in a sense. Category theory is one of several languagues of mathematics, and there are analogies between them. It's kinda like asking "is there a computer program that requires to be written in C?" So I think there is an element of taste whether you prefer category theory to some other (logical) language. That being said, just like in programming, it's still useful to know more than one language, because they potentially have different strengths.