Starting with the ideas of ''some things'' (nodes) and ''some arrows between things'' (arcs), and throwing in a few simple axioms (CategoryTheory), one can construct pretty much all of the maths used in computation; numbers, grammars, the TuringMachine, LambdaCalculus, etc. and so forth. Relational models are already in nodes and arcs, and after a little thought, objects are too. Formally, CategoryTheory is the algebra of functional composition, so FunctionalProgramming falls out of it almost immediately.

In the pure maths field, CategoryTheory can be used to construct set and group theories, and abstract algebras, after which pretty much the whole rest of the subject may be derived. 

Walters' ''Categories and Computer Science'' ISBN: 0521422264 is a good intro for formally-minded IT types.

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I only started to look into this seriously a little while ago - it's one of those subjects that makes my brain itch, which is a feeling I like. -- KeithBraithwaite

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What would a Rule of Inference look like for a graph?

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see also GraphTheory
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