Does anyone know of a book/paper/anything, the longer the better introducing differential geometry from a category theoretic point of view? Everywhere it seems categorical language is the elephant in the room that isn't being addressed fully. I'm looking for something detailed, not just something that says the tangent bundle is a functor, but particularly the relationship between differential geometry constructs and laws in the categories they live in. An exposition on lie groups as well will be great.
My motivation for this is the haskell library manifolds http://hackage.haskell.org/package/manifolds, id like to understand the rational for the author's implementation but of I'd like some reference material
