Substructural fixed-point theorems and the diagonal argument: theme and variations
arXiv:2110.00239 · doi:10.32408/compositionality-5-8
Abstract
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.
v1 20 pages; v2 22 pages, added additional final section on fixed-point operators; v3 final journal version