Categories, Types and Structures. Page 1 HAL Id: hal-03316030 https://ens.hal.science/hal-03316030
Submitted on 10 Aug 2021 HAL is a multi-disciplinary open access archive for the deposit and …

Realizability toposes are" models of constructive set theory" based on abstract notions of
computability. They arose originally in the study of mathematical logic, but since then various …

This paper is concerned with a remarkable fact. The effective topos contains a small
complete subcategory, essentially the familiar category of partial equivalence realtions. This …

Domain theory is the study of various concrete categories C typically of (directed) complete
partial orders in which constructions fundamental to the analysis of computing can be …

Various Theories of Types are introduced, by stressing the analogy 'propositions-as-types':
from propositional to higher order types (and Logic). In accordance with this, proofs are …

The title of this paper ought really to be" Polymorphism can be set theoretic, constructively",
but the obvious reference to Reynolds* paper" Polymorphism is not set theoretic"[R2] was …

Some old and new constructions of free categories with good properties (regularity,
exactness, etc.) are investigated, consistently showing their role in proof theory and in …

We extend the notion of exact completion on a weakly lex category to elementary doctrines.
We show how any such doctrine admits an elementary quotient completion, which freely …

A syntactically rich version of the Coquand-Huet theory of constructions is described as a
theory of dependent types involving expressions at three different levels (Terms, Types and …

It is well known that one can build models of full higher-order dependent-type theory (also
called the calculus of constructions) using partial equivalence relations (PERs) and …