I can't comment on applications of category theory to computer programming or computer science, but I believe that the book Conceptual Mathematics by Lawvere and Schanuel is a nice introduction to the basic ideas of category theory.
I believe this book has been discussed "recently" on HN, but I couldn't find a thread.
Mathematicians write for multiple audiences, but there are two major mathematical audiences for their works: specialists in the same field and researchers in other fields. Phrases like "relatively little mathematical background" normally signal that a work is intended to be accessible to non-specialists, but it's often safe to assume that it is aimed at research mathematicians. I think if a work actually requires relatively little mathematical background, a mathematician is more likely to say something like "no, really, you don't need to know mathematics to understand this!" even when it's not quite true.
I genuinely think you don't need a math background to get a general understanding of category theory, because it's so high level. A lot of it is just drawings, even, not complicated formulae and proofs. It's not category theory itself that's difficult to understand, it's the examples and vocabulary.
I think you really need no more than high school algebra to understand basically what category theory is about.
http://www.cambridge.org/catalogue/catalogue.asp?isbn=978052...
I believe this book has been discussed "recently" on HN, but I couldn't find a thread.
Mathematicians write for multiple audiences, but there are two major mathematical audiences for their works: specialists in the same field and researchers in other fields. Phrases like "relatively little mathematical background" normally signal that a work is intended to be accessible to non-specialists, but it's often safe to assume that it is aimed at research mathematicians. I think if a work actually requires relatively little mathematical background, a mathematician is more likely to say something like "no, really, you don't need to know mathematics to understand this!" even when it's not quite true.