Category theory is relevant to almost everything; blockchainers are just cool enough to realize this.
More seriously, try this:
* [Correct-by-construction Casper: a visualization for the future of blockchain consensus](http://www.rchain.site/?p=88).
It doesn't answer all my questions, but halfway down it says:
> Much of the work for the first two steps of the CBC process have already been done for the case of a distributed, asynchronous, trustless consensus algorithm (details have been uploaded to GitHub). This work was done by Vlad Zamfir in collaboration with Vitalik Buterin, Greg Meredith, and others in a research group initiated by the Ethereum Foundation. In short, the abstract framework represents the protocol itself as a category where the objects are the protocol states and the morphisms are the protocol executions, and defines a function called the “estimator” which maps protocol states onto satisfiable logical propositions about the consensus.
I'm not sure what that means, but it sounds cool.