منابع مشابه
Grothendieck fibrations and classifying spaces
Grothendieck fibrations have played an important role in homotopy theory. Among others, theywereused byThomason to describehomotopy colimits of small categories and byQuillen to derive long exact sequences of higher K-theory groups. We construct simplicial objects, namely the fibred and the cleaved nerve, to characterize the homotopy type of a Grothendieck fibration by using the additional stru...
متن کاملCoarse Geometry via Grothendieck Topologies
In the course of the last years several authors have studied index problems for open Riemannian manifolds. The abstract indices are elements in the K-theory of an associated C∗-algebra, which only depends on the ”coarse” (or large scale) geometry of the underlying metric space. In order to make these indices computable J.Roe introduced a new cohomology theory, called coarse cohomology, which is...
متن کاملGrothendieck Topologies and Ideal Closure Operations
We relate closure operations for ideals and for submodules to non-flat Grothendieck topologies. We show how a Grothendieck topology on an affine scheme induces a closure operation in a natural way, and how to construct for a given closure operation fulfilling certain properties a Grothendieck topology which induces this operation. In this way we relate the radical to the surjective topology and...
متن کاملFpqc Descent and Grothendieck Topologies in a Differential Setting
1.1. Sites. We begin with the underlying idea for a Grothendieck topology. Consider your favorite topological space X. Its topology, don’t use the Zariski topology, is determined by the partially ordered category UX consisting of all the open subsets of X ordered with respect to inclusion. In order to verify that a presheaf is a sheaf on X, we must first construct all possible coverings U = (Ui...
متن کاملCohomology in Grothendieck Topologies and Lower Bounds in Boolean Complexity
This paper is motivated by questions such as P vs. NP and other questions in Boolean complexity theory. We describe an approach to attacking such questions with cohomology, and we show that using Grothendieck topologies and other ideas from the Grothendieck school gives new hope for such an attack. We focus on circuit depth complexity, and consider only finite topological spaces or Grothendieck...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1976
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700024886