Robert L Knighten <RLK@knighten.org> Thursday, March 6, 2008 8:48 am mentioned Semadeni _Banach spaces of continuous functions_ as using a categorical perspective. Maybe that is the book I need. I want to understand Grothendieck's functional analysis in more detail than just to say he used categorical definitions of different tensor products to explain Fredholm kernels. For a start, I know nothing about Fredholm kernels except what is on Wikipedia. Grothendieck's own writings on it are long and start with many definitions so that it is hard for me to see the point -- he even says in Recoltes et Semailles that he never really *felt* the point but did it as an assignment. So that work shows nothing like the very clear motivation he gives for schemes and etale cohomology in SGA. What is a good introduction to his contributions in functional analysis? best, Colin