Lawvere's fixed point theorem is a result in category theory that broadly generalizes many diagonal arguments found across mathematics and logic, including Cantor's diagonal argument, Cantor's theorem, Russell's paradox, Godel's first incompleteness theorem, Turing's solution to the Entscheidungsproblem, and Tarski's undefinability theorem. William Lawvere first proved it in 1969.
Facts
StatementFor any Cartesian closed category C and object B, if there is a weakly point-surjective morphism f from some object A to the exponential object B^A, then every endomorphism g: B -> B has a fixed point. 1 Classification
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Source Lawvere's fixed-point theorem, Wikipedia
Proved By
Source Lawvere's fixed-point theorem, Wikipedia
Sources
1. Lawvere's fixed-point theorem, Wikipedia
Formal statement
Lawvere's theorem states that, for any Cartesian closed category C and given an object B in it, if there is a weakly point-surjective morphism f from some object A to the exponential object B^A, then every endomorphism g: B → B has a fixed point.
Introduction, first proof
It was first proven by William Lawvere in 1969.
In Branch: Category Theory, Lead sentence
e's fixed-point theorem is an important result in category theory.
Proved By: William Lawvere, Lead sentence, attribution
It was first proven by William Lawvere in 1969
In Group: Category Theory, Lead section
Lawvere's fixed-point theorem is an important result in category theory. It is a broad abstract generalization of many
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