category theory

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Logic, Self-Reference, and Category Theory Logic, Self-Reference, and Category Theory
30 min read Keywords:  Gödel, Turing, self-reference, Lawvere, category theory, recursive types, Y combinator

Once arithmetic can encode syntax, a system can act on descriptions of itself. That second engine produces Gödel sentences, quines, the Y combinator, recursive types, and Lawvere’s fixed point theorem.