Related papers: Predicative toposes
In this paper, we identify some categorical structures in which one can model predicative formal systems: in other words, predicative analogues of the notion of a topos, with the aim of using sheaf models to interprete predicative formal…
We give characterizations, for various fragments of geometric logic, of the class of theories classified by a locally connected (resp. connected and locally connected, atomic, compact, presheaf) topos, and exploit the existence of multiple…
As the prototypical category, $\mathbf{Set}$ has many properties which make it special amongst categories. From the point of view of mathematical logic, one such property is that $\mathbf{Set}$ has enough structure to "properly" formalise…
We study toposes of actions of monoids on sets. We begin with ordinary actions, producing a class of presheaf toposes which we characterize. As groundwork for considering topological monoids, we branch out into a study of supercompactly…
In recent work, we introduced a new semantics for conditionals, covering a large class of what we call preconditionals. In this paper, we undertake an axiomatic study of preconditionals and subclasses of preconditionals. We then prove that…
We introduce judgemental theories and their calculi as a general framework to present and study deductive systems. As an exemplification of their expressivity, we approach dependent type theory and natural deduction as special kinds of…
This article gives a conceptual introduction to the topos approach to the formulation of physical theories.
Toposes can be pictured as mathematical universes. Besides the standard topos, in which most of mathematics unfolds, there is a colorful host of alternate toposes in which mathematics plays out slightly differently. For instance, there are…
This paper is the first in a series whose goal is to develop a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise when contemplating quantum theories of…
In this article, we give an unconditional definition of the motivic analogue of the intersection complex, establish its basic properties, and prove its existence in certain cases.
A candidate for the effective 2-topos is proposed and shown to include the effective 1-topos as its subcategory of 0-types.
We present an abstract unifying framework for interpreting Stone-type dualities; several known dualities are seen to be instances of just one topos-theoretic phenomenon, and new dualities are introduced. In fact, infinitely many new…
The classifying topos of a geometric theory is a topos such that geometric morphisms into it correspond to models of that theory. We study classifying toposes for different infinitary logics: first-order, sub-first-order (i.e. geometric…
We describe and compare design choices for meta-predicate semantics, as found in representative Prolog module systems and in Logtalk. We look at the consequences of these design choices from a pragmatic perspective, discussing explicit…
This article is an introduction to the basic generalized category theory used in recent work on an extension of the theory of categories and categorical logic, including parts of topos theory. We discuss functors, equivalences, natural…
In this short note, a topos - called the topos of the connectivity space - is associated with every such space.
We introduce an abstract topos-theoretic framework for building Galois-type theories in a variety of different mathematical contexts; such theories are obtained from representations of certain atomic two-valued toposes as toposes of…
We give necessary and sufficient conditions on a presentable infinity-category C so that families of objects of C form an infinity-topos. In particular, we prove a conjecture of Joyal that this is the case whenever C is stable.
This short expository text is for readers who are confident in basic category theory but know little or nothing about toposes. It is based on some impromptu talks given to a small group of category theorists.
In this paper we introduce and study motives for rational homotopy types.