<?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>S0120-419X2021000200137</article-id>
<article-id pub-id-type="doi">10.18273/revint.v39n2-2021002</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Esqueleto Homoto-Homológico en la Categoría de los Grupos Abelianos]]></article-title>
<article-title xml:lang="en"><![CDATA[Homoto-Homological Skeleton in the Category of Abelian Groups]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[GAITÁN-OSPINA]]></surname>
<given-names><![CDATA[RAFAEL]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad del Valle Departamento de Matemáticas ]]></institution>
<addr-line><![CDATA[Cali ]]></addr-line>
<country>Colombia</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>137</fpage>
<lpage>176</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0120-419X2021000200137&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0120-419X2021000200137&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0120-419X2021000200137&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen. En este artículo, se presenta la construcción de una teoría de homología general en la categoría de los grupos abelianos en el sentido de R. Ruiz, definida en su texto Introducción a la Teoría de Homología General [22], para categorías en general, la cual satisface una axiomática similar a la presentada por Eilenberg y Steenrod para teorías de homología en categorías admisibles de parejas de espacios topológicos (X, A) [3]. Esta teoría de homología general en los grupos abelianos se construyó por medio de un Esqueleto Homoto-Homológico, definido en este trabajo, mostrando sus conexiones con categorías monoidales y categorías simpliciales. MSC2010: 55N10, 20K40.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract. In this paper, we present the construction of a general homology theory in the category of abelian groups in the sense of the textbook Introducción a la Teoría de Homología General by R. Ruiz [22], to general categories, meeting axioms similar to those presented by Eilenberg and Steenrod in homology theories for admissible categories of topological pairs (X, A) [3]. We built this general homology theory in abelian groups through what we called Homoto-Homological Skeleton, showing the connections with monoidal categories and simplicial categories.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Conjuntos simpliciales]]></kwd>
<kwd lng="es"><![CDATA[grupos abelianos simpliciales]]></kwd>
<kwd lng="es"><![CDATA[homotopía]]></kwd>
<kwd lng="es"><![CDATA[homología]]></kwd>
<kwd lng="es"><![CDATA[sistemas homotópicos]]></kwd>
<kwd lng="es"><![CDATA[funtor singular]]></kwd>
<kwd lng="es"><![CDATA[categorías admisibles]]></kwd>
<kwd lng="es"><![CDATA[objeto modelo]]></kwd>
<kwd lng="en"><![CDATA[Simplicial sets]]></kwd>
<kwd lng="en"><![CDATA[simplicial abelian groups]]></kwd>
<kwd lng="en"><![CDATA[homotopy]]></kwd>
<kwd lng="en"><![CDATA[homology]]></kwd>
<kwd lng="en"><![CDATA[homotopic system]]></kwd>
<kwd lng="en"><![CDATA[singular functor]]></kwd>
<kwd lng="en"><![CDATA[admissible categories]]></kwd>
<kwd lng="en"><![CDATA[model object]]></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[Artin]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Braun]]></surname>
<given-names><![CDATA[H]]></given-names>
</name>
</person-group>
<source><![CDATA[Introduction to Algebraic Topology]]></source>
<year>1969</year>
<edition>1</edition>
<publisher-name><![CDATA[Merrill Publishing Company]]></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[Bauer]]></surname>
<given-names><![CDATA[F.W.]]></given-names>
</name>
<name>
<surname><![CDATA[Dugundji]]></surname>
<given-names><![CDATA[J]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Categorical homotopy and fibrations]]></article-title>
<source><![CDATA[Trans. Amer. Math. Soc]]></source>
<year>1969</year>
<volume>140</volume>
<page-range>239-56</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[Eilenberg]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Steenrod]]></surname>
<given-names><![CDATA[N.E]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Axiomatic Approach to Homology Theory]]></article-title>
<source><![CDATA[Proc. Natl. Acad. Sci. USA]]></source>
<year>1945</year>
<volume>31</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>117-20</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[Etingof P.]]></surname>
<given-names><![CDATA[et. al]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Tensor Categories]]></article-title>
<source><![CDATA[American Mathematical Soc]]></source>
<year>2016</year>
<volume>205</volume>
</nlm-citation>
</ref>
<ref id="B5">
<label>[5]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Gabriel]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Zisman]]></surname>
<given-names><![CDATA[M]]></given-names>
</name>
</person-group>
<source><![CDATA[Calculus of Fractions and Homotopy Theory]]></source>
<year>2012</year>
<volume>35</volume>
<publisher-loc><![CDATA[New York ]]></publisher-loc>
<publisher-name><![CDATA[Springer Science &amp; Business Media]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B6">
<label>[6]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Goerss]]></surname>
<given-names><![CDATA[P.G.]]></given-names>
</name>
<name>
<surname><![CDATA[Jardine]]></surname>
<given-names><![CDATA[J.F]]></given-names>
</name>
</person-group>
<source><![CDATA[Simplicial Homotopy Theory]]></source>
<year>2009</year>
<publisher-name><![CDATA[Springer Science &amp; Business Media]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B7">
<label>[7]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Gaitan]]></surname>
<given-names><![CDATA[R]]></given-names>
</name>
</person-group>
<source><![CDATA[Esqueleto Homoto-Homológico En La Categoría De Los Grupos Abelianos]]></source>
<year>2018</year>
<page-range>112p</page-range><publisher-name><![CDATA[Universidad del Valle]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B8">
<label>[8]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hernández]]></surname>
<given-names><![CDATA[L.J]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Un ejemplo de teoría de homotopía en los grupos abelianos]]></article-title>
<source><![CDATA[Collect. Math]]></source>
<year>1982</year>
<volume>33</volume>
<page-range>161-76</page-range></nlm-citation>
</ref>
<ref id="B9">
<label>[9]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hatcher]]></surname>
<given-names><![CDATA[A]]></given-names>
</name>
</person-group>
<source><![CDATA[Algebraic topology]]></source>
<year>2002</year>
<edition>1</edition>
<publisher-name><![CDATA[Cambridge University Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B10">
<label>[10]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hovey]]></surname>
<given-names><![CDATA[M]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Model categories]]></article-title>
<source><![CDATA[Mathematical Surveys and Monographs]]></source>
<year>1999</year>
<volume>63</volume>
</nlm-citation>
</ref>
<ref id="B11">
<label>[11]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hungerford]]></surname>
<given-names><![CDATA[T.W]]></given-names>
</name>
</person-group>
<source><![CDATA[Algebra]]></source>
<year>1974</year>
<volume>73</volume>
<edition>1</edition>
<publisher-loc><![CDATA[New York ]]></publisher-loc>
<publisher-name><![CDATA[Springer-Verlag]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B12">
<label>[12]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hu]]></surname>
<given-names><![CDATA[S.T]]></given-names>
</name>
</person-group>
<source><![CDATA[Homology Theory: a first course in Algebraic Topology]]></source>
<year>1966</year>
<edition>1st</edition>
<publisher-name><![CDATA[Holden-Day]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B13">
<label>[13]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hernández]]></surname>
<given-names><![CDATA[L.J]]></given-names>
</name>
</person-group>
<source><![CDATA[Un Ejemplo de Teoría de Homotopía en los Grupos Abelianos]]></source>
<year>1980</year>
<page-range>232</page-range><publisher-loc><![CDATA[España ]]></publisher-loc>
<publisher-name><![CDATA[Universidad de Zaragoza]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B14">
<label>[14]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kan]]></surname>
<given-names><![CDATA[D.M]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Abstract Homotopy. I]]></article-title>
<source><![CDATA[Proc. Natl. Acad. Sci. USA]]></source>
<year>1955</year>
<volume>41</volume>
<numero>12</numero>
<issue>12</issue>
<page-range>1092-6</page-range></nlm-citation>
</ref>
<ref id="B15">
<label>[15]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kan]]></surname>
<given-names><![CDATA[D.M]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Abstract Homotopy. II]]></article-title>
<source><![CDATA[Proc. Natl. Acad. Sci. USA]]></source>
<year>1956</year>
<volume>42</volume>
<numero>5</numero>
<issue>5</issue>
<page-range>225-8</page-range></nlm-citation>
</ref>
<ref id="B16">
<label>[16]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Leinster]]></surname>
<given-names><![CDATA[T]]></given-names>
</name>
</person-group>
<source><![CDATA[Basic Category Theory]]></source>
<year>2014</year>
<volume>143</volume>
<edition>1</edition>
<publisher-name><![CDATA[Cambridge University Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B17">
<label>[17]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[MacLane]]></surname>
<given-names><![CDATA[S]]></given-names>
</name>
</person-group>
<source><![CDATA[Homology, Classics in mathematics]]></source>
<year>1995</year>
<publisher-loc><![CDATA[Berlin ]]></publisher-loc>
<publisher-name><![CDATA[Springer-Verlag]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B18">
<label>[18]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[May]]></surname>
<given-names><![CDATA[P.J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Simplicial Objects in Algebraic Topology]]></source>
<year>1992</year>
<volume>114</volume>
<publisher-loc><![CDATA[Chicago ]]></publisher-loc>
<publisher-name><![CDATA[University of Chicago Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B19">
<label>[19]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Porter]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
<name>
<surname><![CDATA[Kamps]]></surname>
<given-names><![CDATA[K.H]]></given-names>
</name>
</person-group>
<source><![CDATA[Abstract Homotopy and Simple Homotopy Theory]]></source>
<year>1997</year>
<edition>1st</edition>
<publisher-loc><![CDATA[Singapore ]]></publisher-loc>
<publisher-name><![CDATA[World Scientific]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B20">
<label>[20]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ruiz]]></surname>
<given-names><![CDATA[R]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Overview on models in Homotopical Algebra]]></article-title>
<source><![CDATA[Rev. Acad. Colombiana Cienc. Exact. Fís. Natur]]></source>
<year>2004</year>
<volume>28</volume>
<numero>106</numero>
<issue>106</issue>
<page-range>100-21</page-range></nlm-citation>
</ref>
<ref id="B21">
<label>[21]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ruiz]]></surname>
<given-names><![CDATA[R]]></given-names>
</name>
</person-group>
<source><![CDATA[Change of Models in Algebraic Topology]]></source>
<year>1977</year>
<page-range>311</page-range><publisher-loc><![CDATA[Pennsylvania ]]></publisher-loc>
<publisher-name><![CDATA[Temple University]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B22">
<label>[22]</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ruíz]]></surname>
<given-names><![CDATA[R]]></given-names>
</name>
</person-group>
<source><![CDATA[Introducción a la teoría de homología general]]></source>
<year></year>
</nlm-citation>
</ref>
<ref id="B23">
<label>[23]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Vick]]></surname>
<given-names><![CDATA[J.W]]></given-names>
</name>
</person-group>
<source><![CDATA[Homology Theory: an introduction to algebraic topology]]></source>
<year>1994</year>
<volume>145</volume>
<edition>2</edition>
<publisher-loc><![CDATA[New York ]]></publisher-loc>
<publisher-name><![CDATA[Springer-Verlag]]></publisher-name>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
