A smooth version of the Zariski topos
type: Item
instance of: scholarly article
title: A smooth version of the Zariski topos
zbMATH Open document ID: 0648.18006
DOI: 10.1016/0001-8708(87)90023-5
author: Ieke Moerdijk
author: G. E. Reyes
published in: Advances in Mathematics
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://dspace.library.uu.nl/handle/1874/16732
review text: The category M of (finite-dimensional) smooth manifolds has two limitations: it is not Cartesian closed (in particular, the space of maps between two objects need not be a smooth manifold); there is no convenient language to describe things in the ``infinitely small''. Non- standard analysis initiated by A. Robinson addresses the second limitation, and the theory of differentiable spaces of Chen and the theory of convenient vector spaces of Fröhlicher, Kriger, and others address the first limitation. The aim of the paper under review is to construct a Cartesian closed category L containing M as in the previous approaches. In addition to this, L contains nilpotent and invertible infinitesimals and infinitely large natural numbers. Moreover, L is a Grothendieck topos.
Mathematics Subject Classification ID: 18B25
Mathematics Subject Classification ID: 18D15
Mathematics Subject Classification ID: 58A05
Mathematics Subject Classification ID: 03H05
zbMATH DE Number: 4057751
zbMATH Keywords: category of finite-dimensional smooth manifolds
zbMATH Keywords: Cartesian closed category
zbMATH Keywords: infinitesimals
zbMATH Keywords: Grothendieck topos
reviewed by: L. N. Vaserstein
MaRDI profile type: Publication
OpenAlex ID: W2048753416
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description: scientific article; zbMATH DE number 4057751