By a classifying topos for a first-order theory T, we mean a topos E such that, for any topos F , models of T in F correspond exactly to open geometric morphisms F → E . We show that not every (infinitary) first-order theory has a classifying topos in this sense, but we characterize those which do by an appropriate ‘smallness condition’, and we show that every Grothendieck topos arises as the c...

It is well known that the category of covering projections (that is, locally constant objects) of a locally connected topos is equivalent to the classifying topos of a strict progroupoid (or, equivalently, a localic prodiscrete groupoid), the fundamental progroupoid, and that this progroupoid represents first degree cohomology. In this paper we generalize these results to an arbitrary topos. Th...

It is shown that every topos with enough points is equivalent to the classifying topos of a topological groupoid. 1 Deenitions and statement of the result We recall some standard deenitions ((1, 5, 9]). A topos is a category E which is equivalent to the category of sheaves of sets on a (small) site. Equivalently, E is a topos ii it satisses the Giraud axioms ((1], p. 303). The category of sets ...

In the (covariant) topos approach to quantum theory by Heunen, Landsman and Spitters, one associates to each unital C*-algebra A a topos T (A) of sheaves on a locale and a commutative C*-algebra A within that topos. The Gelfand spectrum of A is a locale Σ in this topos, which is equivalent to a bundle over the base locale. We further develop this external presentation of the locale Σ, by noting...

We propose for the Effective Topos an alternative construction: a realisability framework composed of two levels of abstraction. This construction simplifies the proof that the Effective Topos is a topos (equipped with natural numbers), which is the main issue that this paper addresses. In this our work can be compared to Frey’s monadic tripos-to-topos construction. However, no topos theory or ...

We define a new topos, the Herbrand topos, inspired by the modified realizability topos and our earlier work on Herbrand realizability. We also introduce the category of Herbrand assemblies and characterise these as the ¬¬-separated objects in the Herbrand topos. In addition, we show that the category of sets is included as the category of ¬¬-sheaves and prove that the inclusion functor preserv...

Moerdijk has introduced a topos of sheaves on a category of lters. Following his suggestion, we prove that its double negation subtopos is the topos of sheaves on the subcategory of ultra lters the ultrasheaves. We then use this result to establish a double negation translation of results between the topos of ultrasheaves and the topos on lters. 2000 Mathematics Subject Classi cation. Primary 0...

Context. The goal of the Turn-Off Primordial Stars survey (TOPoS) project is to find and analyse turn-off (TO) stars extremely low metallicity. To select targets for spectroscopic follow-up at high spectral resolution, we relied on low-resolution spectra from Sloan Digital Sky Survey (SDSS). Aims. In this paper, use metallicity estimates obtained our analysis SDSS construct distribution functio...

A locally connected topos is a Galois topos if the Galois objects generate the topos. We show that the full subcategory of Galois objects in any connected locally connected topos is an inversely 2-filtered 2-category, and as an application of the construction of 2-filtered bilimits of topoi, we show that every Galois topos has a point. introduction. Galois topoi (definition 1.5) arise in Grothe...