I'm interested in learning a little smooth infinitesimal analysis. There is a free book by Kock: Smooth Differential Geometry, http://home.imf.au.dk/kock/ . As I dive into it, I feel that I'm not quite sufficiently prepared. He seems to be assuming some category theory and maybe also some knowledge of nonaristotelian logic.
I have copies of Lawvere and Rosebrugh, Sets for Mathematics, and Priest, An Introduction to Non-Classical Logic. It seems like I probably need to read the first $m$ chapters of Lawvere and the first $n$ chapters of Priest. Does this seem about right, and if so, what would be the values of $m$ and $n$? Does $n=0$? Amazon will let you see the table of contents of the two books with their "click to look inside" feature:
I have browsed the beginning of the Priest book and found it enjoyable, but haven't solved any of the problems. Category theory seemed dull and pointless to me, which is why I haven't really tackled much of Lawvere -- but maybe the light will dawn and some point and I'll realize why I should care about the subject.
If anyone wants to suggest replacing Kock, Lawvere, or Priest with some other book, that would be fine. I'm not hoping to become technically adept in smooth infinitesimal analysis, just to understand the basic ideas. Is there much of a distinction between smooth infinitesimal analysis, which is what I want to know about, and the subject of Kock's book, whose title says it's about smooth differential geometry?
Does this subject relate to topos theory?
[EDIT] It sounds like I may want to read Bell, A Primer of Infinitesimal Analysis rather than Kock.