A Synopsis of Morphoid Type Theory

Morphoid type theory (MTT) is a typetheoretic foundation for mathematics supporting the concept of isomorphism and the substitution of isomorphics. Unlike homotopy type theory (HoTT), which also supports isomorphism, morphoid type theory is a direct extension of classical predicate calculus and avoids the intuitionistic constructs of propositionsas-types, path induction and squashing. Although HoTT is capable of supporting classical inference, MTT’s thoroughly classical treatment is expected to be more comfortable for those who take a Platonic or realist approach to the practice of mathematics.