J. Funk. The display locale of a cosheaf. Cahiers de Top. et Geom. Di#. Categoriques, 36(1):53--93, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....locally componentwise constant objects. The notion of a spread is closely related to the one introduced by R.H.Fox [13] for topological spaces. In fact, this notion is already cast in terms of the frames of opens of a topological space and therefore translates without change to locales (but see [14]) A continuous map p: Y X of locales, where Y is assumed locally connected, is said to be a spread if the components of the p (U ) for u 2 O(X) form a basis for O(Y ) A spread as above is said to be a complete spread if the cosheaf F : O(X) S de ned as the composite 0 p , where 0 : ....

.... a spread if the components of the p (U ) for u 2 O(X) form a basis for O(Y ) A spread as above is said to be a complete spread if the cosheaf F : O(X) S de ned as the composite 0 p , where 0 : O(Y ) S is the connected components functor, is completely determined by p in this manner(see [14], 10] for details) Proposition 26 Let Y be a locally componentwise constant object in a locally connected topos E. Then, Y is a complete spread object in E. PROOF. It is shown in [10] that any locally constant object in a locally connected topos E is a complete spread object in E. Virtually ....

J. Funk, The display locale of a cosheaf, Cahiers de Top. Geo. Di. Cat. 36-1 (1995) 53-93.

....this groupoid are taken to be the elements of the branch point set of the ramified cover. One of our goals is to show how these groupoids are involved in braid group orderings. In particular, we describe an order structure that a ramification groupoid carries. Our approach involves cosheaf spaces [12], which we review in 2. Cosheaf spaces are defined by an adjointness with cosheaves, but they have a topological characterization that is almost equivalent to Fox s notion of a complete spread. Fox had introduced complete spreads as a framework by which to study topologically ramified covers. It ....

....# 1 (X U ) is a directed graph with an involution, but as we have said it may not have a law of composition. When we use # 1 (X) with no subscript on X, we shall mean the ordinary fundamental groupoid. 2. Review of cosheaf spaces and complete spreads We review the notion of cosheaf space [12] and the slightly more general notion of complete spread, due to R. Fox. Our terminology is a mixture coming from [2, 11, 12] We first review complete spreads. Following [11] a spread is a continuous map # : Y ## X, where Y is locally connected, such that the components of sets # 1 (U ) for U ....

[Article contains additional citation context not shown here]

J. Funk. The display locale of a cosheaf. Cahiers de Top. et Geom. Di#. Categoriques, 36(1):53--93, 1995.

....0. INTRODUCTION By an S valued distribution on a topos E bounded over a base topos S it is meant here a cocontinuous S indexed functor : E S. Since introduced by F. W. Lawvere in 1983, considerable progress has been made in the study of distributions on toposes from a variety of viewpoints [19, 15, 24, 5, 6, 12, 7, 8, 9]. However, much work still remains to be done in this area. The purpose of this paper is to deepen our understanding of topos distributions by exploring a (dual) lattice theoretic notion of distribution algebra. We characterize the distribution algebras in E relative to S as the S bicomplete ....

....algebra. We characterize the distribution algebras in E relative to S as the S bicomplete S atomic Heyting algebras in E . As an illustration, we employ distribution algebras explicitly in order to give an alternative description of the display locale (complete spread) of a distribution [10, 12, 7]. We also prove, under a certain hypothesis on E (satis ed for instance by all Grothendieck toposes or by all essential localizations of any topos of internal presheaves) that the opposite of the category of distributions on E is monadic over E by means of a double dualization monad. Our results ....

[Article contains additional citation context not shown here]

J. Funk, The display locale of a cosheaf, Cahiers de Top. et Geom. Di. Categoriques 36-1 (1995) 53-93.

....Technische Universit at Darmstadt Schlo gartenstrs.7, 64289 Darmstadt, Germany Dedicated to Max Kelly on the occasion of his 70th Birthday 1 2 BUNGE FUNK JIBLADZE STREICHER Abstract. We continue the investigation of the extension into the topos realm of the concepts introduced by R.H. Fox [10] and E.Michael [22] in connection with topological singular coverings. In particular, we construct an analogue of the Michael completion of a spread and compare it with the analogue of the Fox completionobtained earlier by the rst two named authors [4] Two ingredients are present in our ....

....measures on E whose analysis we do not pursue here. We close the paper with several other open questions and directions for future work. 2000 Mathematics Subject Classi cation 18B35, 18F20, 54B30, 18A32, 55R55, 55R70. 0. INTRODUCTION The notion of a complete spread was introduced by R.H. Fox [10] as a common generalization of two di erent types of coverings with singularities (branched and folded) A di erent notion of a proper spread was given by E. Michael [22] in connection with topological cuts. In both cases, the basic idea is that of a spread, meaning a continuous map : Y X of ....

J. Funk, The display locale of a cosheaf, Cahiers Top. et Geometrie Di. Categoriques 36 (1995) 53-93.

....transformation x t , where Sh(X) x Gamma S is the point distribution determined by x. The points of a locale carry in a natural way a topology. In the case of D, the open sets of this topology, U; ff) f(x; t) j x 2 U and t U = ffg; U open in X; ff 2 U ; describe the display space [11] of . The display space illustrates a link with the topological notion of complete spread since a natural transformation x t amounts to a consistent choice ft U 2 U = d Ug of components of inverse images under of neighbourhoods U of x. When X is a complete metric space, D is always ....

....a link with the topological notion of complete spread since a natural transformation x t amounts to a consistent choice ft U 2 U = d Ug of components of inverse images under of neighbourhoods U of x. When X is a complete metric space, D is always spatial. It has been shown [11] that over a complete metric space X, the category of complete spreads in Fox s sense (with locally connected and T 1 domain) is equivalent to the category of complete spreads over Sh(X) in the sense of Definition 1.1. Theory and Applications of Categories, Vol. 7, No. 1 4 2. The Lebesgue ....

[Article contains additional citation context not shown here]

J. Funk. The display locale of a cosheaf. Cahiers de Top. et G'eom. Diff. Cat'egoriques, 36(1):53--93, 1995.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC