Diagonal Arguments and Cartesian Closed Categories
Book Chapter
Formal Antecedent
Category Theory
Citation
F. William Lawvere. (1969). Diagonal Arguments and Cartesian Closed Categories. Category Theory, Homology Theory and Their Applications II. 92. pp. 134–145. Springer.
Why this reference is included
Lawvere’s chapter Diagonal Arguments and Cartesian Closed Categories (1969) in Category Theory, Homology Theory and Their Applications II sits in the program’s reference corpus. Cited across Book I (Categorical Foundations), Part 18, Chapter The Self-Hosting Landscape; Book I (Categorical Foundations), Part 18, Chapter Star-Autonomous Categories and the Diagonal Barrier — the central framing is “Lawvere (1969). Lawvere’s fixed-point theorem provides the categorical distillation”.
Cited in
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Book I — Categorical Foundations Part 18Chapter The Self-Hosting Landscape
Lawvere (1969). Lawvere's fixed-point theorem provides the categorical distillation
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Book I — Categorical Foundations Part 18Chapter Star-Autonomous Categories and the Diagonal Barrier
In 1969, Lawvere proved the following : in a cartesian closed category, if there exists a point-surjection e : A → B^A — meaning that for every g : A → B, there exists a_0 : 1 → A such that e ∘ a_0 = g (where g is the transpose of g) — then every endomorphism f : B → B has a fixed point