I keep trying to get the gist of type theory and it's like eating unflavored jello.
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E.g. it’s hard for me to imagine how homotopy, which is about continuous deformations of continuous functions, could give leverage in ToC, where nothing is continuous. Presumably I’m missing something because I haven’t even bothered to look this up, but
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To make an analogy: Euclid's Axioms :: Real Cartesian Plane as Homotopy Type Theory :: Spaces of various sorts. We work up to homotopy equivalence, so all the data you care about can be presented combinatorially...
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