Applications of category theory and topoi/topos theory in reality

I wrote a reply to a related question describing applications of category theory to programming, but it's on http://mathoverflow.net I could copy it here, but that might not be considered ethical so here is a link.

Also, check out the work by David Spivak on categorical databases.

I can present you with a personal example.

I am creating a mathematical model which independently lends itself to a algebraic interpretation using the Dirac's Bra-Ket notation and also could be visualized as a digraph.

So up until a few months ago, I was having real troubles placing the fundamental model upon which these two viewpoints presented themselves as one entity. They came from the same phenomenology and they purport to describe the same, so which one was better and which one should I focus on to really understand what was going on?

Category theory made that question obsolete when I realized that both of these incarnations were mere categorical reflections of an overlying categorical space. Thus I realized that the algebra was a cograph and digraphs where the graph (as Lawvere and Schnuel define a cograph in Conceptual Math p. 280) and my work has taken off since! :)