Exact subcategories of the category of locally convex spaces
Identifieur interne : 001103 ( Istex/Corpus ); précédent : 001102; suivant : 001104Exact subcategories of the category of locally convex spaces
Auteurs : Bernhard Dierolf ; Dennis SiegSource :
- Mathematische Nachrichten [ 0025-584X ] ; 2012-12.
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Abstract
In this paper we present a characterization whether the restriction \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal {E}^{\prime }:=\lbrace (f,g)\in \mathcal {E}\,\,|\,\,f,g\in \mbox{Mor}({\mathcal {C}}^{\prime })\rbrace$\end{document} of the exact structure \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal {E}$\end{document} of an exact category \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$({\mathcal {C}},\mathcal {E})$\end{document} in the sense of Quillen on a full additive subcategory \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathcal {C}}^{\prime }$\end{document} of \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathcal {C}}$\end{document} is again an exact structure. We apply our characterization to the exact structure \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal {E}^{top}_{\mbox{LCS}}$\end{document} of short topologically exact sequences in the quasi‐abelian category \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mbox{LCS}$\end{document} of locally convex spaces and subcategories thereof.
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DOI: 10.1002/mana.201100325
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Nachr.</title><idno type="ISSN">0025-584X</idno><idno type="eISSN">1522-2616</idno><imprint><publisher>WILEY‐VCH Verlag</publisher><pubPlace>Germany</pubPlace><date type="published" when="2012-12">2012-12</date><biblScope unit="volume">285</biblScope><biblScope unit="issue">17‐18</biblScope><biblScope unit="page" from="2106">2106</biblScope><biblScope unit="page" to="2119">2119</biblScope></imprint><idno type="ISSN">0025-584X</idno></series><idno type="istex">2D038EC601A2D5DF73E8E15138DF5BE48362D42F</idno><idno type="DOI">10.1002/mana.201100325</idno><idno type="ArticleID">MANA201100325</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0025-584X</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>18E10</term><term>18G50</term><term>46A13</term><term>46M18</term><term>MSC (2010)</term><term>Three‐space‐property</term><term>exact structure</term><term>topologically exact sequences</term></keywords></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">In this paper we present a characterization whether the restriction \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal {E}^{\prime }:=\lbrace (f,g)\in \mathcal {E}\,\,|\,\,f,g\in \mbox{Mor}({\mathcal {C}}^{\prime })\rbrace$\end{document} of the exact structure \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal {E}$\end{document} of an exact category \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$({\mathcal {C}},\mathcal {E})$\end{document} in the sense of Quillen on a full additive subcategory \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathcal {C}}^{\prime }$\end{document} of \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathcal {C}}$\end{document} is again an exact structure. We apply our characterization to the exact structure \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal {E}^{top}_{\mbox{LCS}}$\end{document} of short topologically exact sequences in the quasi‐abelian category \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mbox{LCS}$\end{document} of locally convex spaces and subcategories thereof.</div></front></TEI><istex><corpusName>wiley</corpusName><author><json:item><name>Bernhard Dierolf</name><affiliations><json:string>FB IV Mathematics, University of Trier, 54286 Trier, Germany</json:string><json:string>Bernhard Dierolf, Phone: +49 651 201 3509, Fax: +49 651 201 3961Dennis Sieg, Phone: +49 651 201 3509, Fax: +49 651 201 3961</json:string></affiliations></json:item><json:item><name>Dennis Sieg</name><affiliations><json:string>FB IV Mathematics, University of Trier, 54286 Trier, Germany</json:string><json:string>Bernhard Dierolf, Phone: +49 651 201 3509, Fax: +49 651 201 3961Dennis Sieg, Phone: +49 651 201 3509, Fax: +49 651 201 3961</json:string></affiliations></json:item></author><subject><json:item><lang><json:string>eng</json:string></lang><value>Three‐space‐property</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>exact structure</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>topologically exact sequences</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>MSC (2010)</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>18E10</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>18G50</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>46M18</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>46A13</value></json:item></subject><articleId><json:string>MANA201100325</json:string></articleId><language><json:string>eng</json:string></language><originalGenre><json:string>article</json:string></originalGenre><abstract>In this paper we present a characterization whether the restriction \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal {E}^{\prime }:=\lbrace (f,g)\in \mathcal {E}\,\,|\,\,f,g\in \mbox{Mor}({\mathcal {C}}^{\prime })\rbrace$\end{document} of the exact structure \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal {E}$\end{document} of an exact category \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$({\mathcal {C}},\mathcal {E})$\end{document} in the sense of Quillen on a full additive subcategory \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathcal {C}}^{\prime }$\end{document} of \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathcal {C}}$\end{document} is again an exact structure. We apply our characterization to the exact structure \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal {E}^{top}_{\mbox{LCS}}$\end{document} of short topologically exact sequences in the quasi‐abelian category \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mbox{LCS}$\end{document} of locally convex spaces and subcategories thereof.</abstract><qualityIndicators><score>5.96</score><pdfVersion>1.3</pdfVersion><pdfPageSize>594 x 792 pts</pdfPageSize><refBibsNative>true</refBibsNative><abstractCharCount>1255</abstractCharCount><pdfWordCount>7052</pdfWordCount><pdfCharCount>34824</pdfCharCount><pdfPageCount>14</pdfPageCount><abstractWordCount>80</abstractWordCount></qualityIndicators><title>Exact subcategories of the category of locally convex spaces</title><refBibs><json:item><author><json:item><name>K. D. Bierstedt</name></json:item><json:item><name>J. 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KGaA, Weinheim</p></availability><date>2012</date></publicationStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a" type="main" xml:lang="en">Exact subcategories of the category of locally convex spaces</title><author xml:id="author-1"><persName><forename type="first">Bernhard</forename><surname>Dierolf</surname></persName><affiliation>FB IV Mathematics, University of Trier, 54286 Trier, Germany</affiliation><affiliation>Bernhard Dierolf, Phone: +49 651 201 3509, Fax: +49 651 201 3961Dennis Sieg, Phone: +49 651 201 3509, Fax: +49 651 201 3961</affiliation></author><author xml:id="author-2"><persName><forename type="first">Dennis</forename><surname>Sieg</surname></persName><affiliation>FB IV Mathematics, University of Trier, 54286 Trier, Germany</affiliation><affiliation>Bernhard Dierolf, Phone: +49 651 201 3509, Fax: +49 651 201 3961Dennis Sieg, Phone: +49 651 201 3509, Fax: +49 651 201 3961</affiliation></author></analytic><monogr><title level="j">Mathematische Nachrichten</title><title level="j" type="abbrev">Math. Nachr.</title><idno type="pISSN">0025-584X</idno><idno type="eISSN">1522-2616</idno><idno type="DOI">10.1002/(ISSN)1522-2616</idno><imprint><publisher>WILEY‐VCH Verlag</publisher><pubPlace>Germany</pubPlace><date type="published" when="2012-12"></date><biblScope unit="volume">285</biblScope><biblScope unit="issue">17‐18</biblScope><biblScope unit="page" from="2106">2106</biblScope><biblScope unit="page" to="2119">2119</biblScope></imprint></monogr><idno type="istex">2D038EC601A2D5DF73E8E15138DF5BE48362D42F</idno><idno type="DOI">10.1002/mana.201100325</idno><idno type="ArticleID">MANA201100325</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>2012</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>In this paper we present a characterization whether the restriction \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal {E}^{\prime }:=\lbrace (f,g)\in \mathcal {E}\,\,|\,\,f,g\in \mbox{Mor}({\mathcal {C}}^{\prime })\rbrace$\end{document} of the exact structure \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal {E}$\end{document} of an exact category \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$({\mathcal {C}},\mathcal {E})$\end{document} in the sense of Quillen on a full additive subcategory \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathcal {C}}^{\prime }$\end{document} of \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathcal {C}}$\end{document} is again an exact structure. We apply our characterization to the exact structure \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal {E}^{top}_{\mbox{LCS}}$\end{document} of short topologically exact sequences in the quasi‐abelian category \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mbox{LCS}$\end{document} of locally convex spaces and subcategories thereof.</p></abstract><textClass xml:lang="en"><keywords scheme="keyword"><list><head>keywords</head><item><term>Three‐space‐property</term></item><item><term>exact structure</term></item><item><term>topologically exact sequences</term></item><item><term>MSC (2010)</term></item><item><term>18E10</term></item><item><term>18G50</term></item><item><term>46M18</term></item><item><term>46A13</term></item></list></keywords></textClass><textClass><keywords scheme="Journal Subject"><list><head>article-category</head><item><term>Original Paper</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="2011-11-20">Received</change><change when="2012-06-01">Registration</change><change when="2012-12">Published</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><extension>txt</extension><original>false</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/document/2D038EC601A2D5DF73E8E15138DF5BE48362D42F/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="Wiley, elements deleted: body"><istex:xmlDeclaration>version="1.0" encoding="UTF-8" standalone="yes"</istex:xmlDeclaration><istex:document><component version="2.0" type="serialArticle" xml:lang="en"><header><publicationMeta level="product"><publisherInfo><publisherName>WILEY‐VCH Verlag</publisherName><publisherLoc>Germany</publisherLoc></publisherInfo><doi registered="yes">10.1002/(ISSN)1522-2616</doi><issn type="print">0025-584X</issn><issn type="electronic">1522-2616</issn><idGroup><id type="product" value="MANA"></id></idGroup><titleGroup><title type="main" xml:lang="de" sort="MATHEMATISCHE NACHRICHTEN">Mathematische Nachrichten</title><title type="short">Math. 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KGaA, Weinheim</copyright><eventGroup><event type="manuscriptReceived" date="2011-11-20"></event><event type="manuscriptRevised" date="2012-03-27"></event><event type="manuscriptAccepted" date="2012-06-01"></event><event type="xmlConverted" agent="Converter:JWSART34_TO_WML3G version:3.1.9 mode:FullText mathml2tex" date="2012-11-29"></event><event type="publishedOnlineEarlyUnpaginated" date="2012-08-13"></event><event type="firstOnline" date="2012-08-13"></event><event type="publishedOnlineFinalForm" date="2012-11-29"></event><event type="xmlConverted" agent="Converter:WILEY_ML3G_TO_WILEY_ML3GV2 version:3.8.8" date="2014-02-02"></event><event type="xmlConverted" agent="Converter:WML3G_To_WML3G version:4.3.4 mode:FullText" date="2015-02-24"></event></eventGroup><numberingGroup><numbering type="pageFirst">2106</numbering><numbering type="pageLast">2119</numbering></numberingGroup><correspondenceTo><lineatedText><line>Bernhard Dierolf, Phone: +49 651 201 3509, Fax: +49 651 201 3961</line><line>Dennis Sieg, Phone: +49 651 201 3509, Fax: +49 651 201 3961</line></lineatedText></correspondenceTo><linkGroup><link type="toTypesetVersion" href="file:MANA.MANA201100325.pdf"></link></linkGroup></publicationMeta><contentMeta><countGroup><count type="figureTotal" number="0"></count><count type="tableTotal" number="0"></count><count type="referenceTotal" number="36"></count></countGroup><titleGroup><title type="main" xml:lang="en">Exact subcategories of the category of locally convex spaces</title><title type="short" xml:lang="en">Exact subcategories</title></titleGroup><creators><creator xml:id="au1" creatorRole="author" affiliationRef="#af1" corresponding="yes"><personName><givenNames>Bernhard</givenNames><familyName>Dierolf</familyName></personName><contactDetails><email normalForm="dier4501@uni-trier.de">dier4501@uni‐trier.de</email></contactDetails></creator><creator xml:id="au2" creatorRole="author" affiliationRef="#af1" corresponding="yes"><personName><givenNames>Dennis</givenNames><familyName>Sieg</familyName></personName><contactDetails><email>dsieg80@googlemail.com</email></contactDetails></creator></creators><affiliationGroup><affiliation xml:id="af1" countryCode="DE" type="organization"><unparsedAffiliation>FB IV Mathematics, University of Trier, 54286 Trier, Germany</unparsedAffiliation></affiliation></affiliationGroup><keywordGroup xml:lang="en" type="author"><keyword xml:id="kwd1">Three‐space‐property</keyword><keyword xml:id="kwd2">exact structure</keyword><keyword xml:id="kwd3">topologically exact sequences</keyword><keyword xml:id="kwd4"><b>MSC (2010)</b></keyword><keyword xml:id="kwd5">18E10</keyword><keyword xml:id="kwd6">18G50</keyword><keyword xml:id="kwd7">46M18</keyword><keyword xml:id="kwd8">46A13</keyword></keywordGroup><abstractGroup><abstract type="main" xml:lang="en"><title type="main">Abstract</title><p>In this paper we present a characterization whether the restriction <span type="latex">\documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal {E}^{\prime }:=\lbrace (f,g)\in \mathcal {E}\,\,|\,\,f,g\in \mbox{Mor}({\mathcal {C}}^{\prime })\rbrace$\end{document}</span> of the exact structure <span type="latex">\documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal {E}$\end{document}</span> of an exact category <span type="latex">\documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$({\mathcal {C}},\mathcal {E})$\end{document}</span> in the sense of Quillen on a full additive subcategory <span type="latex">\documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathcal {C}}^{\prime }$\end{document}</span> of <span type="latex">\documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathcal {C}}$\end{document}</span> is again an exact structure. We apply our characterization to the exact structure <span type="latex">\documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal {E}^{top}_{\mbox{LCS}}$\end{document}</span> of short topologically exact sequences in the quasi‐abelian category <span type="latex">\documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mbox{LCS}$\end{document}</span> of locally convex spaces and subcategories thereof.</p></abstract></abstractGroup></contentMeta></header></component></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Exact subcategories of the category of locally convex spaces</title></titleInfo><titleInfo type="abbreviated" lang="en"><title>Exact subcategories</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Exact subcategories of the category of locally convex spaces</title></titleInfo><name type="personal"><namePart type="given">Bernhard</namePart><namePart type="family">Dierolf</namePart><affiliation>FB IV Mathematics, University of Trier, 54286 Trier, Germany</affiliation><affiliation>Bernhard Dierolf, Phone: +49 651 201 3509, Fax: +49 651 201 3961Dennis Sieg, Phone: +49 651 201 3509, Fax: +49 651 201 3961</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Dennis</namePart><namePart type="family">Sieg</namePart><affiliation>FB IV Mathematics, University of Trier, 54286 Trier, Germany</affiliation><affiliation>Bernhard Dierolf, Phone: +49 651 201 3509, Fax: +49 651 201 3961Dennis Sieg, Phone: +49 651 201 3509, Fax: +49 651 201 3961</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="article" displayLabel="article"></genre><originInfo><publisher>WILEY‐VCH Verlag</publisher><place><placeTerm type="text">Germany</placeTerm></place><dateIssued encoding="w3cdtf">2012-12</dateIssued><dateCaptured encoding="w3cdtf">2011-11-20</dateCaptured><dateValid encoding="w3cdtf">2012-06-01</dateValid><copyrightDate encoding="w3cdtf">2012</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType><extent unit="references">36</extent></physicalDescription><abstract lang="en">In this paper we present a characterization whether the restriction \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal {E}^{\prime }:=\lbrace (f,g)\in \mathcal {E}\,\,|\,\,f,g\in \mbox{Mor}({\mathcal {C}}^{\prime })\rbrace$\end{document} of the exact structure \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal {E}$\end{document} of an exact category \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$({\mathcal {C}},\mathcal {E})$\end{document} in the sense of Quillen on a full additive subcategory \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathcal {C}}^{\prime }$\end{document} of \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathcal {C}}$\end{document} is again an exact structure. We apply our characterization to the exact structure \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal {E}^{top}_{\mbox{LCS}}$\end{document} of short topologically exact sequences in the quasi‐abelian category \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mbox{LCS}$\end{document} of locally convex spaces and subcategories thereof.</abstract><subject lang="en"><genre>keywords</genre><topic>Three‐space‐property</topic><topic>exact structure</topic><topic>topologically exact sequences</topic><topic>MSC (2010)</topic><topic>18E10</topic><topic>18G50</topic><topic>46M18</topic><topic>46A13</topic></subject><relatedItem type="host"><titleInfo><title>Mathematische Nachrichten</title></titleInfo><titleInfo type="abbreviated"><title>Math. 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