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On the Structure of Zero Morphisms in a Quasi-Pointed Category

Applied Categorical Structures volume 25, pages 1037–1043 (2017)Cite this article

Abstract

A quasi-pointed category in the sense of D. Bourn is a finitely complete category \(\mathcal {C}\) having an initial object such that the unique morphism from the initial object to the terminal object is a monomorphism. When instead this morphism is an isomorphism, we obtain a (finitely complete) pointed category, and as it is well known, the structure of zero morphisms in a pointed category determines an enrichment of the category in the category of pointed sets. In this note we examine quasi-pointed categories through the structure formed by the zero morphisms (i.e. the morphisms which factor through the initial object), with the aim to compare this structure with an enrichment in the category of pointed sets.

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Authors and Affiliations

  1. Department of Mathematics and Applied Mathematics, University of Limpopo, Turfloop Campus, Private Bag X1106, Sovenga, 0727, South Africa

    Amartya Goswami

  2. Mathematics Division, Department of Mathematical Sciences, Stellenbosch University, Private Bag X1, Matieland, 7602, South Africa

    Zurab Janelidze

Authors
  1. Amartya Goswami
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  2. Zurab Janelidze
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Corresponding author

Correspondence to Amartya Goswami.

Additional information

The first author acknowledges the support of the University of Limpopo. The second author acknowledges the support of the South African National Research Foundation.

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Goswami, A., Janelidze, Z. On the Structure of Zero Morphisms in a Quasi-Pointed Category. Appl Categor Struct 25, 1037–1043 (2017). https://doi.org/10.1007/s10485-016-9462-y

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  • DOI: https://doi.org/10.1007/s10485-016-9462-y

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