The lambda calculus was originally conceived by Church (1932 1933) as part of a general
theory of functions and logic, intended as a foundation for mathematics. Although the full …

We present a categorical logic formulation of induction and coinduction principles for
reasoning about inductively and coinductively defined types. Our main results provide …

A comprehension category is defined as a functor P: E→ B→ satisfying (a) a cod∘ P is a
fibration, and (b) f is cartesian in E implies that P f is a pullback in B. This notion captures …

An elementary topological approach to Grothendieck's idea of descent is given. While being
motivated by the idea of localization which is central in Sheaf Theory, we show how the …

Within the framework of categorical logic or categorical type theory, predicate logics and
type theories are understood as fibrations with structure. Fibrations, or fibred categories …

We consider some basic properties of the 2-category Fib of fibrations over arbitrary bases,
exploiting the fact that it is fibred over Cat. We show a factorisation property for adjunctions …

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 …

This paper studies presheaf models for concurrent computation. An aim is to harness the
general machinery around presheaves for the purposes of process calculi. Traditional …

Logic is the study of reasoning. Typically, it proceeds in terms of inferring a conclusion from
established premises. The systematic use of symbolic and mathematical techniques to …

In the first part of the thesis, we suggest a general notion of realizability, based on weakly
closed partial cartesian categories, which generalizes the usual notion of realizability over a …