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- PETER JOHNSTONE
- 2011

We study the condition, on a connected and locally connected geometric morphism p : E → S, that the canonical natural transformation p * → p ! should be (pointwise) epimorphic — a condition which F.W. Lawvere [11] called the 'Nullstellen-satz', but which we prefer to call 'punctual local connectedness'. We show that this condition implies that p ! preserves… (More)

Image-guided radiation therapy delivery may be used to assess the position of the tumor and anatomical structures within the body as opposed to relying on external marks. The purpose of this manuscript is to evaluate the performance of the image registration software for automatically detecting and repositioning a 3D offset of a phantom using a kilovoltage… (More)

Each full reeective subcategory X of a nitely-complete category C gives rise to a factorization system (E; M) on C, where E consists of the morphisms of C inverted by the reeexion I : C ! X. Under a simplifying assumption which is satissed in many practical examples, a morphism f : A ! B lies in M precisely when it is the pullback along the unit B : B ! IB… (More)

In the literature there are several kinds of concrete and abstract cell complexes representing composition in n-categories, ω-categories or ∞-categories, and the slightly more general partial ω-categories. Some examples are parity complexes, pasting schemes and directed complexes. In this paper we give an axiomatic treatment: that is to say, we study the… (More)

Preframes (directed complete posets with finite meets that distribute over the directed joins) are the algebras for an infinitary essentially algebraic theory, and can be presented by generators and relations. This result is combined with a general argument concerning categories of commutative monoids to give a very short proof of the localic Tychonoff… (More)

MOTIVATION
Microarray experiments with thousands of genes on a slide and multiple slides used in any experimental set represent a large body of data with many sources of variation. The identification of such sources of variation within microarray experimental sets is critical for correct deciphering of desired gene expression differences.
RESULTS
We… (More)

- PETER JOHNSTONE
- 1999

The class of functors known as discrete Conduché fibrations forms a common generalization of discrete fibrations and discrete opfibrations, and shares many of the formal properties of these two classes. F. Lamarche [7] conjectured that, for any small category B, the category DCF/B of discrete Conduché fibrations over B should be a topos. In this note we… (More)

- PETER JOHNSTONE
- 2013

We show that every geometric morphism between realizability toposes satisfies the condition that its inverse image commutes with the 'constant object' func-tors, which was assumed by John Longley in his pioneering study of such morphisms. We also provide the answer to something which was stated as an open problem on Jaap van Oosten's book on realizability… (More)

- PETER JOHNSTONE
- 2013

Recently Benno van den Berg [1] introduced a new class of realizability toposes which he christened Herbrand toposes. These toposes have strikingly different properties from ordinary realizability toposes, notably the (related) properties that the 'constant object' functor from the topos of sets preserves finite coproducts, and that De Morgan's law is… (More)

We prove that certain categories arising from atoms in a Grothendieck topos are themselves Grothendieck toposes. We also investigate enrichments of these categories over the base topos; there are in fact often two distinct enrichments.