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### Contents

Geometric invariance of existential fixedpoint logic | 9 |

On the decidability of objects in a locos | 23 |

The Dialectica categories | 48 |

Copyright | |

13 other sections not shown

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### Common terms and phrases

2-category arrow atomic axioms Beck-Chevalley condition bicategory bijection bilimit binary cartesian closed category category of models category theory clauses cocones coherent comonad comonoid composition Computer Science condition cones consists corresponding defined definition denote domain E-topos Editors elements equality equations equivalent example existential fixed-point exists exponentials extensionality fact fibration formulas full subcategory function geometric morphism Girard given graph homomorphism Grothendieck hence idempotent inclusion induced internal interpretation intuitionistic isomorphism judgements lambda calculus lambda terms language left adjoint Lemma lex category lex functor lim theory linear logic locos Mathematics means monoidal category multicategory natural numbers natural transformation notation notion operation pair polymorphic lambda poset preserves proof Proposition pullback recursive rewrite rules right adjoint satisfies semantics sequents sketch homomorphism structure subobject symbols syntactic terminal object Theorem theory of constructions topos type theory typed lambda unique