Fucking Whatever Tournament - Round 1
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Homotopy Type Theory
Innocent Tyrant
Homotopy: Recent development in proof theory, a domain at the intersection of computer science, math, logic, topology and category theory. It stems from problems coming from the definition of equality in higher-order intuitionistic logics. The central paradigm is to interpret elements of a type as points, equality as paths between points, and types as topological spaces. The main contribution is the "Univalence Axiom", which state that two types are equal if and only if they are equivalent. In computer words: two types that behave the same are the same. This theory has very deep developments that I don't fully understand, but trust me, it's dope!
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