This article re-examines Lawvere's abstract, category-theoretic proof of the fixed-point theorem whose contrapositive is a `universal' diagonal argument. The main result is that the necessary axioms for both the fixed-point theorem and the diagonal argument can be stripped back further, to a semantic analogue of a weak substructural logic lacking weakening or exchange.

翻译：本文重新审视了Lawvere的范畴论抽象不动点定理证明，其逆否命题构成了“通用”对角线论证。主要结果表明，不动点定理与对角线论证所需的公理可进一步精简至弱子结构逻辑的语义类似物，该逻辑缺乏弱化或交换规则。