The Maximality of the Typed Lambda Calculus and of Cartesian Closed Categories

Details The Maximality of the Typed Lambda Calculus and of Cartesian Closed Categories The Maximality of the Typed Lambda Calculus and of Cartesian Closed Categories

1999-11-11

arxiv.org/abs/math/9911073v1

Mathematics

Category Theory

21 pages, to appear in Publications de l'Institut Mathematique

Scientific paper

From the analogue of Boehm's Theorem proved for the typed lambda calculus, without product types and with them, it is inferred that every cartesian closed category that satisfies an equality between arrows not satisfied in free cartesian closed categories must be a preorder. A new proof is given here of these results, which were obtained previously by Richard Statman and Alex K. Simpson.

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