This sentence doesn't really make sense, insofar as TFA isn't about some conjecture.
I meant to say "also a proof of this".
What is "this?" The paper uses category theory as its lingua franca.
Relationship between computation, logic and topology.
In this context it's probably wise to use "proof" carefully, otherwise it's easy to confuse with its mathematical usage. Maybe "Homotopy type theory is also a sign of the relationship between computation, logic and topology" is a better way to express what you were trying to say :)