I am an amateur mathematician with an interest in the subjects named in the title. I have recently come to understand that my B.A. in math gives me absolutely no qualification at all in the Swedish job market. Hence I will try to compliment it with something else. I'd like to remain as close as I can to the pure world so now I'm wondering if anybody has any idea of related yet practical fields.
Edit: I am thinking (very vaguely) that there might be something along the lines of organizing database into functional and searchable structures.
Regards,
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.