I have a basic working knowledge of category thoery since I do research in programming languages and typed lambda-calculus. Indeed, I have refereed many papers in my area based on category theory.


But, in doing this refereeing, and in reading many important categorial papers in my area, I simply find the terminology and presentation style extremely opaque compared to style that I prefer which instead emphasizes logic inference rules and extensions of the lambda calculus.


Given the (extended) Curry-Howard Isomorphism between programming languages, logics, and categories, it's clear that I can understand the concepts I need by mapping category theory into the other two. But, am I missing something in the process, or are the papers I'm refereeing just making things more difficult than they need to be? 



Why do I find Category Theory mostly just a way to make simple things difficult?
Although to you, category theory is merely an inefficient framework for data about logic and programming languages, to mathematicians working in areas like algebraic geometry and algebraic topology, categories are truly essential. For us, some of our most basic notions make no sense and look extremely awkward (in fact, some of them are from pre-category days, and no one really knew what we wanted intuitively until after we started using categories) until you phrase them in terms of categories and universal properties of objects and morphisms (and 2-morphisms, etc). Additionally, it helps us tell what various types of mathematical objects have in common, and how they relate via functors and natural transformations.


As far as recasting algebraic topology and algebraic geometry in terms of lambda calculus, I'd rather like to see that if anyone can manage to, say, give an alternative definition of stack or gerbe or model structure which are more intuitive without using categories and groupoids and the like.


