Calibrated toposes
type: Item
instance of: scholarly article
title: Calibrated toposes
zbMATH Open document ID: 1266.18007
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 2013-01-17T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.bbms/1354031555
review text: This rather technical paper focuses on the description of the relationship between the slice categories \(\varepsilon/A\), \(A\) being an object of the elementary topos \(\varepsilon\), and the corresponding topos of sheaves on \(A\), hereafter called the petit topos on \(A\). The idea is to consider \(\varepsilon\), the gros topos, as a space of spaces, the petit toposes. Essentially, a petit topos on \(A\) is the full subcategory of \(\varepsilon/A\) whose objects we may think as fibrewise discrete morphisms with codomain \(A\); a calibration is an attempt to axiomatise this notion. Although many fundamental properties of calibrations are derived in the article, together with a few examples, the work is not yet conclusive: not all the objects of a gros topos are sufficiently spacelike to be represented up to homotopy equivalence by their petit toposes. An analysis on how to characterize those objects which have this property is left to a subsequent work. In conclusion, this paper describes a very technical result which is still partial. Thus, the work is of interest mainly for specialists in the theory of toposes, both because of the required technical level, and because of the intermediate nature of the achievements.
reviewed by: Marco Benini
Mathematics Subject Classification ID: 18B25
zbMATH DE Number: 6126475
zbMATH Keywords: topos
zbMATH Keywords: calibration
zbMATH Keywords: locally connected morphism
zbMATH Keywords: local morphism
author: Peter Johnstone
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6126475