bibkey: lawvere1969diagonal authors: F. William Lawvere year: 1969 title: Diagonal arguments and cartesian closed categories doi: 10.1007/BFb0080769 claim: Diagonal self-application yields the qualitative fixed-point principle for point-surjective maps. strata_touched:

• D5/S0/Diagonal/EscapeCount
• D5/S0/Diagonal/CaptureCount license: citation-only triage: anchor

Diagonal Arguments and Cartesian Closed Categories

F. William Lawvere gives a categorical fixed-point theorem whose set-level specialization is the familiar diagonal argument: point-surjectivity of an evaluation map forces every endomorphism of the codomain to have a fixed point. The repository’s landing lemma records the local implication used by that argument when a listed row equals its twisted diagonal.

The source does not state the repository’s finite cardinality formula. The exact number of escaped listings is therefore not attributed to Lawvere; it is deposited as repository-derived kernel truth, and its relation to prior literature remains an open question tracked by this note’s search log.

Search log

• 2026-08-06: The frozen implementation brief supplied the author, year, exact title, and Lecture Notes in Mathematics volume 92. The DOI recorded here is the Springer chapter locator. No online metadata query was run in the restricted implementation worker.

Locator

• DOI: https://doi.org/10.1007/BFb0080769