We discuss some ways in which topos theory (a branch of category theory) can be applied to interpretative problems in quantum theory and quantum gravity. In Section 1, we introduce these problems. In Section 2, we introduce topos theory, especially the idea of a topos of presheaves. In Section 3, we discuss several possible applications of topos theory to the problems in Section 1. In Section 4...

We present a way of constructing a Quillen model structure on a full subcategory of an elementary topos, starting with an interval object with connections and a certain dominance. The advantage of this method is that it does not require the underlying topos to be cocomplete. The resulting model category structure gives rise to a model of homotopy type theory with identity types, Σand Π-types, a...

with regard to the essential role and function of topos / place (in comparison with time) in the thinking, acting and speaking of the ancient individuals, it is possible to analyze the inscribed speeches of ancient persian kings according to their conceptions of topos or place. for reaching to this aim darius' inscriptions in behistun (db) will be chosen and they will be analyzed within an appr...

We place simple axioms on an elementary topos which suf-ce for it to provide a denotational model of call-by-value PCF with sum and product types. The model is synthetic in the sense that types are interpreted by their set-theoretic counterparts within the topos. The main result characterises when the model is computationally adequate with respect to the operational semantics of the programming...

We determine the points of the epicyclic topos which plays a key role in the geometric encoding of cyclic homology and the lambda operations. We show that the category of points of the epicyclic topos is equivalent to projective geometry in characteristic one over algebraic extensions of the infinite semifield of “max-plus integers” Zmax. An object of this category is a pair (E,K) of a semimodu...

Let 6 e be an elementary topos. The axiom of infinity, asserting that 5 e has a natural numbers object, is shown to be necessary-sufficiency has long been k n o w n f o r the existence of an object-classifying topos over 5 e. In the known constructions [1, 4, 6] of classifying topoi for geometric theories, it is always assumed that the base topos fie satisfies the axiom of infinity. The purpose...

Let Φ′ be a non-Gaussian, affine subring. It was Lindemann who first asked whether ultra-closed, Siegel functors can be extended. We show that there exists a reducible, unique and Möbius ω-compact topos. It is not yet known whether h > z, although [23] does address the issue of naturality. Next, recently, there has been much interest in the derivation of quasi-covariant elements.

Isham’s topos-theoretic perspective on the logic of the consistent-histories theory [34] is extended in two ways. First, the presheaves of consistent sets of history propositions in their corresponding topos originally proposed in [34] are endowed with a Vietoristype of topology and subsequently they are sheafified with respect to it. The category resulting from this sheafification procedure is...

This paper defines a solution manifold and a stable submanifold for a system of differential equations. Although we eventually work in the smooth topos, the first two sections do not mention topos theory and should be of interest to non-topos theorists. The paper characterizes solutions in terms of barriers to growth and defines solutions in what are called filter rings (characterized as C∞-red...

Given a partial combinatory algebra (pca) A (see e.g. [16]) together with a subpca A# of A we will construct the nested realizability topos RT(A,A#) as described in [5] (without giving it a proper name there). It is well known (from e.g. [16]) that RT(A,A#) appears as the exact/regular completion of its subcategory Asm(A,A#) of assemblies. In [5] the authors considered two complementary subtopo...