<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-00492424</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-26T09:01:53+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="it">A convenient differential category</title>
            <author role="aut">
              <persName>
                <forename type="first">Richard</forename>
                <surname>Blute</surname>
              </persName>
              <email type="md5">a26670a6697670644852d885c03e4eb1</email>
              <email type="domain">uottawa.ca</email>
              <idno type="idhal" notation="numeric">872113</idno>
              <idno type="halauthorid" notation="string">470229-872113</idno>
              <affiliation ref="#struct-210701"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Thomas</forename>
                <surname>Ehrhard</surname>
              </persName>
              <email type="md5">ed475c91ccd26a8f518e16547b8d21be</email>
              <email type="domain">irif.fr</email>
              <idno type="idhal" notation="string">thomas-ehrhard</idno>
              <idno type="idhal" notation="numeric">742157</idno>
              <idno type="halauthorid" notation="string">45101-742157</idno>
              <idno type="ORCID">https://orcid.org/0000-0001-5231-5504</idno>
              <idno type="IDREF">https://www.idref.fr/132983664</idno>
              <affiliation ref="#struct-1067"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Christine</forename>
                <surname>Tasson</surname>
              </persName>
              <email type="md5">3643613bf542081c9229977998ae60a6</email>
              <email type="domain">lip6.fr</email>
              <idno type="idhal" notation="numeric">865456</idno>
              <idno type="halauthorid" notation="string">398167-865456</idno>
              <idno type="ORCID">https://orcid.org/0000-0001-8098-9944</idno>
              <idno type="IDREF">https://www.idref.fr/142544108</idno>
              <affiliation ref="#struct-40199"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Christine</forename>
                <surname>Tasson</surname>
              </persName>
              <email type="md5">0f4e3d0b75f6cb44ff4eb5efd770fd03</email>
              <email type="domain">isae-supaero.fr</email>
            </editor>
            <funder ref="#projanr-3437"/>
            <funder>NSERC Discovery Grant</funder>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2010-06-15 18:02:52</date>
              <date type="whenWritten">2010-05-27</date>
              <date type="whenModified">2026-01-07 15:07:09</date>
              <date type="whenReleased">2010-06-16 08:58:37</date>
              <date type="whenProduced">2010-05-27</date>
              <date type="whenEndEmbargoed">2010-06-15</date>
              <ref type="file" target="https://hal.science/hal-00492424v1/document">
                <date notBefore="2010-06-15"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-00492424v1/file/BET.pdf" id="file-492424-667412">
                <date notBefore="2010-06-15"/>
              </ref>
              <ref type="externalLink" target="http://arxiv.org/pdf/1006.3140"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="146243">
                <persName>
                  <forename>Christine</forename>
                  <surname>Tasson</surname>
                </persName>
                <email type="md5">0f4e3d0b75f6cb44ff4eb5efd770fd03</email>
                <email type="domain">isae-supaero.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-00492424</idno>
            <idno type="halUri">https://hal.science/hal-00492424</idno>
            <idno type="halBibtex">blute:hal-00492424</idno>
            <idno type="halRefHtml">2010</idno>
            <idno type="halRef">2010</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-492424-667412"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="CEA">CEA - Commissariat à l'énergie atomique</idno>
            <idno type="stamp" n="UNIV-PARIS7" corresp="UNIV-PARIS">Université Denis Diderot - Paris VII</idno>
            <idno type="stamp" n="PPS">Laboratoire Preuves, Programmes et Systèmes</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="DRT" corresp="CEA">Direction de la recherche technologique</idno>
            <idno type="stamp" n="LIST" corresp="CEA">Laboratoire d'Intégration des Systèmes et des Technologies</idno>
            <idno type="stamp" n="UNIV-PARIS">Université Paris Cité</idno>
            <idno type="stamp" n="ANR">ANR</idno>
            <idno type="stamp" n="GS-SPORT-HUMAN-MOVEMENT">Graduate School Sport, Mouvement, Facteurs Humains</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="1">Not set</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="it">A convenient differential category</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Richard</forename>
                    <surname>Blute</surname>
                  </persName>
                  <email type="md5">a26670a6697670644852d885c03e4eb1</email>
                  <email type="domain">uottawa.ca</email>
                  <idno type="idhal" notation="numeric">872113</idno>
                  <idno type="halauthorid" notation="string">470229-872113</idno>
                  <affiliation ref="#struct-210701"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Thomas</forename>
                    <surname>Ehrhard</surname>
                  </persName>
                  <email type="md5">ed475c91ccd26a8f518e16547b8d21be</email>
                  <email type="domain">irif.fr</email>
                  <idno type="idhal" notation="string">thomas-ehrhard</idno>
                  <idno type="idhal" notation="numeric">742157</idno>
                  <idno type="halauthorid" notation="string">45101-742157</idno>
                  <idno type="ORCID">https://orcid.org/0000-0001-5231-5504</idno>
                  <idno type="IDREF">https://www.idref.fr/132983664</idno>
                  <affiliation ref="#struct-1067"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Christine</forename>
                    <surname>Tasson</surname>
                  </persName>
                  <email type="md5">3643613bf542081c9229977998ae60a6</email>
                  <email type="domain">lip6.fr</email>
                  <idno type="idhal" notation="numeric">865456</idno>
                  <idno type="halauthorid" notation="string">398167-865456</idno>
                  <idno type="ORCID">https://orcid.org/0000-0001-8098-9944</idno>
                  <idno type="IDREF">https://www.idref.fr/142544108</idno>
                  <affiliation ref="#struct-40199"/>
                </author>
              </analytic>
              <monogr>
                <imprint/>
              </monogr>
              <idno type="arxiv">1006.3140</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="it">convenient vector spaces</term>
                <term xml:lang="it">denotational semantics</term>
                <term xml:lang="it">differential linear logic</term>
              </keywords>
              <classCode scheme="halDomain" n="info.info-lo">Computer Science [cs]/Logic in Computer Science [cs.LO]</classCode>
              <classCode scheme="halDomain" n="math.math-lo">Mathematics [math]/Logic [math.LO]</classCode>
              <classCode scheme="halTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halOldTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halTreeTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>In this paper, we show that the category of Mackey-complete, separated, topological convex bornological vector spaces and bornological linear maps is a differential category. Such spaces were introduced by Frölicher and Kriegl, where they were called convenient vector spaces. While much of the structure necessary to demonstrate this observation is already contained in Frölicher and Kriegl's book, we here give a new interpretation of the category of convenient vector spaces as a model of the differential linear logic of Ehrhard and Regnier. Rather than base our proof on the abstract categorical structure presented by Frölicher and Kriegl, we prefer to focus on the bornological structure of convenient vector spaces. We believe bornological structures will ultimately yield a wide variety of models of differential logics.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-210701" status="VALID">
          <orgName>Departement of Mathematics and Statistics [Ottawa, University of Ottawa]</orgName>
          <desc>
            <address>
              <addrLine>University of Ottawa, 585 King Edward, Ottawa, Ontario, K1N 6N5, Canada</addrLine>
              <country key="CA"/>
            </address>
            <ref type="url">https://www.uottawa.ca/faculty-science/mathematics-statistics</ref>
          </desc>
          <listRelation>
            <relation active="#struct-237693" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-1067" status="OLD">
          <orgName>Preuves, Programmes et Systèmes</orgName>
          <orgName type="acronym">PPS</orgName>
          <date type="end">2015-12-31</date>
          <desc>
            <address>
              <addrLine>Université Paris Diderot, Bât. Sophie Germain, case postale 7014, 75205 Paris Cedex 13</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.pps.univ-paris-diderot.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300301" type="direct"/>
            <relation name="UMR7126" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="researchteam" xml:id="struct-40199" status="VALID">
          <orgName>Laboratoire Modélisation et Analyse de Systèmes en Interaction</orgName>
          <orgName type="acronym">LMeASI</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation name="DRT/LIST" active="#struct-40217" type="direct"/>
            <relation name="DRT/LIST" active="#struct-440043" type="indirect"/>
            <relation name="DRT" active="#struct-300016" type="indirect"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-237693" status="VALID">
          <idno type="IdRef">026431343</idno>
          <idno type="ROR">https://ror.org/03c4mmv16</idno>
          <orgName>University of Ottawa [Ottawa]</orgName>
          <desc>
            <address>
              <addrLine>75 Laurier Avenue East, Ottawa, ON K1N 6N5</addrLine>
              <country key="CA"/>
            </address>
            <ref type="url">http://www.uottawa.ca</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-300301" status="OLD">
          <idno type="IdRef">027542084</idno>
          <idno type="ISNI">0000000121514068</idno>
          <idno type="ROR">https://ror.org/02n7qrg46</idno>
          <orgName>Université Paris Diderot - Paris 7</orgName>
          <orgName type="acronym">UPD7</orgName>
          <date type="end">2019-12-31</date>
          <desc>
            <address>
              <addrLine>5 rue Thomas-Mann - 75205 Paris cedex 13</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-paris-diderot.fr</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
        <org type="laboratory" xml:id="struct-40217" status="VALID">
          <idno type="IdRef">156836882</idno>
          <idno type="ISNI">0000 0004 0405 1788</idno>
          <idno type="RNSR">200118591H</idno>
          <idno type="ROR">https://ror.org/000dbcc61</idno>
          <idno type="Wikidata">Q30299467</idno>
          <orgName>Laboratoire d'Intégration des Systèmes et des Technologies</orgName>
          <orgName type="acronym">LIST (CEA)</orgName>
          <desc>
            <address>
              <addrLine>DRT/LISTNano-INNOVAvenue de la Vauve91120 Palaiseau</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www-list.cea.fr/</ref>
          </desc>
          <listRelation>
            <relation name="DRT/LIST" active="#struct-440043" type="direct"/>
            <relation name="DRT" active="#struct-300016" type="indirect"/>
          </listRelation>
        </org>
        <org type="regrouplaboratory" xml:id="struct-440043" status="VALID">
          <idno type="IdRef">067087930</idno>
          <idno type="ISNI">0000000121157881</idno>
          <idno type="RNSR">199018589D</idno>
          <idno type="ROR">https://ror.org/02ggzyd20</idno>
          <idno type="Wikidata">Q30299418</idno>
          <orgName>Direction de Recherche Technologique (CEA)</orgName>
          <orgName type="acronym">DRT (CEA)</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.drt-cea.com/</ref>
          </desc>
          <listRelation>
            <relation name="DRT" active="#struct-300016" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-300016" status="VALID">
          <idno type="IdRef">026372061</idno>
          <idno type="ISNI">0000000122998025</idno>
          <idno type="ROR">https://ror.org/00jjx8s55</idno>
          <idno type="Wikidata">Q868550</idno>
          <orgName>Commissariat à l'énergie atomique et aux énergies alternatives</orgName>
          <orgName type="acronym">CEA</orgName>
          <desc>
            <address>
              <addrLine>Centre de SaclayCentre de GrenobleCentre de Cadaracheetc</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.cea.fr/</ref>
          </desc>
        </org>
      </listOrg>
      <listOrg type="projects">
        <org type="anrProject" xml:id="projanr-3437" status="VALID">
          <idno type="anr">ANR-07-BLAN-0324</idno>
          <idno type="program">Blanc</idno>
          <orgName>CHOCO</orgName>
          <desc>Curry-Howard pour la concurrence</desc>
          <date type="start">2007</date>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>