A Survey on Lawvere's Fixed-Point Theorem (2025) (opens in new tab)

This paper provides an overview of Lawvere's Fixed-Point Theorem in category theory and aims to detail the universal framework underlying self-reference and recursive structures. First, we rigorously define fundamental concepts - such as terminal objects, products, Cartesian Closed Categories, exponential objects, evaluation maps, currying, and point-surjective morphisms - and explain their intuitive meanings through concrete examples and commutative diagrams. Based on these foundational noti...