I am trying to understand Kant's taxonomy of ideas (or "representations") and I am stuck on his meaning of "intuition", in particular, whether or not the object of an intuition always refers to something that is empirically real. My working interpretation of "object" is something like "the thing that the thought is about", and hence could refer to something that can be given in experience or not (like the things studied in math). That he does mean that the objects of intuitions always refer to material things in the world is suggested to me in how he says that these objects must be "given to us" through our sensibility and that these intuitions are acquired through the way objects "affect" us.

If I restrict to thinking only about external objects in the world affecting my senses, then I think I can understand what he means well enough, but once I start contemplating other forms of thought I get confused as to the difference between objects and ideas. For example, if I dream up some object in my mind that doesn't exist in the world, like a chair or a triangle, but nonetheless think it singularly and picture it in my mind, is this an intuition? If so, what is the object and how do you distinguish it from the idea itself?