A natural fibration for rings
type: Item
instance of: scholarly article
title: A natural fibration for rings
zbMATH Open document ID: 1497.16046
DOI: 10.4171/RSMUP/76
author: Alessandro Andrea Bosi
author: Alberto Facchini
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 2021-07-02T00:00:00Z
review text: The authors study the functors between several categories, the most important of which are the category Ring of all (associative, unital) rings, the category ParOrd\(_0\) of all partially ordered sets with the least element, and the category RingedParOrd\(_0\) of all ringed partially ordered sets with the least element. A ringed partially ordered set (with the least element) is a pair \((L, F)\), where \(L\) is a partially ordered set (with the least element) and \(F:L\rightarrow\) Ring is a covariant functor.\par Ringed partially ordered sets are similar to ringed spaces. The results of the present paper are versions of the results known for ringed spaces to the case of ringed partially ordered sets.\par The authors construct contravariant functors \({\mathcal H}:\) Ring\(\rightarrow\) RingedParOrd\(_0\) and \(Z:\) RingedParOrd\(_0\rightarrow\) Ring such that \(Z\circ{\mathcal H}=1_{\mathrm{Ring}}\), but \(\mathcal H\) and \(Z\) are not adjoint on the right and not adjoint on the left.\par In the last chapter, the authors construct a fibration \(p:\)RingedParOrd\(_0\rightarrow\) ParOrd\(_0\), which is actually a projection functor.
Mathematics Subject Classification ID: 16W80
Mathematics Subject Classification ID: 16B50
Mathematics Subject Classification ID: 18B35
zbMATH DE Number: 7367435
zbMATH Keywords: ringed space
zbMATH Keywords: fibred category
zbMATH Keywords: Zariski spectrum of a ring
reviewed by: Mart Abel
MaRDI profile type: Publication
cites work: Coproducts and Some Universal Ring Constructions
cites work: Q4848757
cites work: On a partially ordered set associated to ring morphisms
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cites work: On category \(\mathcal O\) for the rational Cherednik algebra of \(G(m,1,n)\): the almost semisimple case.
full work available at URL: https://doi.org/10.4171/rsmup/76
OpenAlex ID: W3159149184
description: scientific article; zbMATH DE number 7367435