<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0120-419X</journal-id>
<journal-title><![CDATA[Revista Integración]]></journal-title>
<abbrev-journal-title><![CDATA[Integración - UIS]]></abbrev-journal-title>
<issn>0120-419X</issn>
<publisher>
<publisher-name><![CDATA[Universidad Industrial de Santander]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0120-419X2021000200241</article-id>
<article-id pub-id-type="doi">10.18273/revint.v39n2-2021006</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Induced (&#8496;, &#8499;)-structures on Topological Categories]]></article-title>
<article-title xml:lang="es"><![CDATA[(&#8496;, &#8499;)-estructuras inducidas en categorías topológicas]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[ANGOA-AMADOR]]></surname>
<given-names><![CDATA[JUAN]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[CONTRERAS-CARRETO]]></surname>
<given-names><![CDATA[AGUSTÍN]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[GONZÁLEZ-SANDOVAL]]></surname>
<given-names><![CDATA[JESÚS]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Benemérita Universidad Autónoma de Puebla Facultad de Ciencias Físico Matemáticas ]]></institution>
<addr-line><![CDATA[Puebla ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Benemérita Universidad Autónoma de Puebla Facultad de Ciencias Físico Matemáticas ]]></institution>
<addr-line><![CDATA[Puebla ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Benemérita Universidad Autónoma de Puebla Facultad de Ciencias Físico Matemáticas ]]></institution>
<addr-line><![CDATA[Puebla ]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2021</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2021</year>
</pub-date>
<volume>39</volume>
<numero>2</numero>
<fpage>241</fpage>
<lpage>256</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0120-419X2021000200241&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0120-419X2021000200241&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0120-419X2021000200241&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract. In this paper, we describe a convenient categorical structure with respect to a class of monomorphisms &#8499; and epimorphisms E for any topo-logical category. We show in particular that the structure that we introduce here, which is induced by topological functors and their initial liftings, allows the study of some &#8499; - coreflective subcategories of a topological category. We pay special attention to projective structures. MSC2010: 18A20, 18A32, 18G05, 54A05, 55U40.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen. En este artículo describimos una estructura categórica conveniente respecto a una clase de monomorfismos &#8499; y una clase de epimorfismos E, para cada categoría topológica. En particular, mostramos que la estructura que introducimos aquí, que es inducida por functores topológicos y levantamientos iniciales, permite el estudio de algunas subcategorías &#8499; -correflexivas de una categoría topológica. Prestamos atención especial a estructuras proyectivas.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[(&#8496;]]></kwd>
<kwd lng="en"><![CDATA[&#8499;)-category]]></kwd>
<kwd lng="en"><![CDATA[initial lift]]></kwd>
<kwd lng="en"><![CDATA[topological category]]></kwd>
<kwd lng="en"><![CDATA[topological functor]]></kwd>
<kwd lng="es"><![CDATA[Categoría topológica]]></kwd>
<kwd lng="es"><![CDATA[(&#8496;]]></kwd>
<kwd lng="es"><![CDATA[&#8499;)- categoría]]></kwd>
<kwd lng="es"><![CDATA[funtor topológico]]></kwd>
<kwd lng="es"><![CDATA[levantamiento inicial]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<label>[1]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Adámek]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Herrlich]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
<name>
<surname><![CDATA[Strecker]]></surname>
<given-names><![CDATA[G.E]]></given-names>
</name>
</person-group>
<source><![CDATA[Abstract and Concrete Categories: The Joy of Cats]]></source>
<year>1990</year>
<publisher-loc><![CDATA[New York ]]></publisher-loc>
<publisher-name><![CDATA[Wiley]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B2">
<label>[2]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Castellini]]></surname>
<given-names><![CDATA[G]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Connectedness with Respect to a Closure Operator]]></article-title>
<source><![CDATA[Appl. Categ. Structures]]></source>
<year>2001</year>
<volume>9</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>285-302</page-range></nlm-citation>
</ref>
<ref id="B3">
<label>[3]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Clementino]]></surname>
<given-names><![CDATA[M.M]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On Connectedness via Closure Operators]]></article-title>
<source><![CDATA[Appl. Categ. Structures]]></source>
<year>2001</year>
<volume>9</volume>
<numero>6</numero>
<issue>6</issue>
<page-range>539-56</page-range></nlm-citation>
</ref>
<ref id="B4">
<label>[4]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Dikranjan]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Giuli]]></surname>
<given-names><![CDATA[E]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Closure operators I]]></article-title>
<source><![CDATA[Topology Appl]]></source>
<year>1987</year>
<volume>27</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>129-43</page-range></nlm-citation>
</ref>
<ref id="B5">
<label>[5]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Dikranjan]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Tholen]]></surname>
<given-names><![CDATA[W]]></given-names>
</name>
</person-group>
<source><![CDATA[Categorical Structure of Closure Operators]]></source>
<year>1995</year>
<volume>346</volume>
<edition>1</edition>
<publisher-loc><![CDATA[Dordrecht ]]></publisher-loc>
<publisher-name><![CDATA[Springer Netherlands]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B6">
<label>[6]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Freyd]]></surname>
<given-names><![CDATA[P]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Aspects of topoi]]></article-title>
<source><![CDATA[Bull. Aust. Math. Soc]]></source>
<year>1972</year>
<volume>7</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>1-76</page-range></nlm-citation>
</ref>
<ref id="B7">
<label>[7]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Herrlich]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
<name>
<surname><![CDATA[Strecker]]></surname>
<given-names><![CDATA[G.E]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Coreflective subcategories]]></article-title>
<source><![CDATA[Trans. Amer. Math. Soc]]></source>
<year>1971</year>
<volume>157</volume>
<page-range>205-26</page-range></nlm-citation>
</ref>
<ref id="B8">
<label>[8]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Herrlich]]></surname>
<given-names><![CDATA[H]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Reflexionen und Coreflexionen]]></article-title>
<source><![CDATA[Topologische Reflexionen und Coreflexio-nen (ed.Dold and Eckmann)]]></source>
<year>1968</year>
<page-range>76-113</page-range><publisher-name><![CDATA[Springer-Verlag Berlin]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B9">
<label>[9]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Herrlich]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Limit-operators and topological coreflections]]></article-title>
<source><![CDATA[Trans. Amer. Math. Soc]]></source>
<year>1969</year>
<volume>146</volume>
<page-range>203-10</page-range></nlm-citation>
</ref>
<ref id="B10">
<label>[10]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Herrlich]]></surname>
<given-names><![CDATA[H]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Topological Functors]]></article-title>
<source><![CDATA[Topology Appl]]></source>
<year>1974</year>
<volume>4</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>125-42</page-range></nlm-citation>
</ref>
<ref id="B11">
<label>[11]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Isbell]]></surname>
<given-names><![CDATA[J.R]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Subobjects, adequacy, completeness and categories of algebras]]></article-title>
<source><![CDATA[Instytut Matematyczny Polskiej Akademi Nauk (Warszawa)]]></source>
<year>1964</year>
<numero>36</numero>
<issue>36</issue>
<page-range>3-32</page-range></nlm-citation>
</ref>
<ref id="B12">
<label>[12]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kelly]]></surname>
<given-names><![CDATA[G.M]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Monomorphisms, epimorphisms, and pull-backs]]></article-title>
<source><![CDATA[J. Aust. Math. Soc]]></source>
<year>1969</year>
<volume>9</volume>
<numero>1-2</numero>
<issue>1-2</issue>
<page-range>124-42</page-range></nlm-citation>
</ref>
<ref id="B13">
<label>[13]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[MacLane]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Moerdijk]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
</person-group>
<source><![CDATA[Sheaves in Geometry and Logic]]></source>
<year>1994</year>
<edition>1st</edition>
<publisher-loc><![CDATA[New York ]]></publisher-loc>
<publisher-name><![CDATA[Springer-Verlag]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B14">
<label>[14]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Nakagawa]]></surname>
<given-names><![CDATA[R]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Chapter 14 categorical topology]]></article-title>
<source><![CDATA[Topics in General Topology (ed. Morita and Nagata.)]]></source>
<year>1989</year>
<page-range>563-623</page-range><publisher-name><![CDATA[Elsevier]]></publisher-name>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
