{
  "abstract": "We study Hopfian and co-Hopfian objects in an abelian category and in the category of complex sequences of morphisms. Among other results, it is shown that if $X$ and $Y$ are two objects of a category $\\mathscr{A}$ and $\\operatorname{Hom}_{\\mathscr{A}}(X, Y)$ is a co-Hopfian object such that every morphism in $\\operatorname{Hom}_{\\mathscr{A}}(X, Y)$ is a monomorphism, then $X$ is Hopfian; and if every morphism in $\\operatorname{Hom}_{\\mathscr{A}}(X, Y)$ is an epimorphism, then $Y$ is co-Hopfian. Furthermore, if $\\mathscr{A}$ is a balanced abelian category, $X$ is a projective object of $\\mathscr{A}$ satisfying for every $A \\in O b(\\mathscr{A}), A \\neq 0_{\\mathscr{A}}$ implies $\\operatorname{Hom}_{\\mathscr{A}}(X, A) \\neq\\left\\{e_{X, A}\\right\\}$, and $(Y, \\beta) \\in \\operatorname{Ob}(\\operatorname{Comp}(\\mathscr{A}))$ is such that $\\operatorname{Hom}_{\\operatorname{Comp}(\\mathscr{A})}(X,(Y, \\beta))$ is Hopfian, then $(Y, \\beta)$ is Hopfian. And, if $\\mathscr{A}$ is a balanced abelian category, $Y$ is an injective object of $\\mathscr{A}$, and $(X, \\alpha) \\in O b(\\operatorname{Comp}(\\mathscr{A}))$ is such that $\\operatorname{Hom}_{\\operatorname{Comp}(\\mathscr{A})}((X, \\alpha), Y)$ is co-Hopfian, then $(X, \\alpha)$ is co-Hopfian.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "name": "Ablaye Diallo"
    },
    {
      "name": "Mohamed Ben Maaouia"
    },
    {
      "name": "Mamadou Sanghare"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a4888ffrrs1ee.bib",
  "cited_by": 0,
  "doi": "10.17654/0972555526041",
  "fulltext_url": null,
  "id": "a4888ffrrs1ee",
  "issns": [
    "0972-5555"
  ],
  "landing_url": "https://hal.science/hal-05840267v1",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7171101440",
  "pdf_url": "https://pphmjopenaccess.com/jpjana/article/download/4224/3404",
  "pmcid": null,
  "pmid": null,
  "published": "2026-07-25",
  "publisher": "Pushpa Publishing House",
  "ris": "https://research.draconitic.com/paper/a4888ffrrs1ee.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:01Z",
      "native_id": "hal-05840267",
      "source": "hal",
      "url": "https://hal.science/hal-05840267v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2608|Algebraic structures and combinatorial models",
      "subfield": "geometry-topology"
    }
  ],
  "title": "ON HOPFIAN AND CO-HOPFIAN OBJECTS IN AN ABELIAN CATEGORY AND IN THE CATEGORY OF ITS COMPLEX SEQUENCES OF MORPHISMS",
  "title_text": "ON HOPFIAN AND CO-HOPFIAN OBJECTS IN AN ABELIAN CATEGORY AND IN THE CATEGORY OF ITS COMPLEX SEQUENCES OF MORPHISMS",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:01Z",
  "url": "https://research.draconitic.com/paper/a4888ffrrs1ee",
  "venue": "JP Journal of Algebra, Number Theory and Applications",
  "versions": []
}