Roberts, D.M.2023-08-162023-08-162023Compositionality, 2023; 5(8):1-162631-4444https://hdl.handle.net/2440/139139This 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.enThis Paper is published in Compositionality under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.math.CTcs.LOmath.LO03B47, 18A15F.4.1Journal article10.32408/compositionality-5-82023-08-12591346Roberts, D.M. [0000-0002-3478-0522]