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Universal Monos in Partial Morphism Categories

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Abstract

In this paper the category, of partial morphisms of a category \(\mathcal{C}\) with respect to a certain class \(\mathcal{D}\) of subobjects of \(\mathcal{C}\) is formed and the universality of monomorphisms of \({\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {\mathcal{C}} }\) is investigated. The main result characterizes \({\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {\mathcal{C}} }\)-universality of monos, in terms of \(\mathcal{C}\)-universality of monos and the existence of local \(\mathcal{C}\)-implications.

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Authors and Affiliations

  1. Mathematics Department, Shahid Bahonar University of Kerman, Kerman, Iran

    S. N. Hosseini

  2. Mathematics Department, University of Miami, Miami, FL, USA

    M. V. Mielke

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  1. S. N. Hosseini
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  2. M. V. Mielke
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Correspondence to S. N. Hosseini.

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Hosseini, S.N., Mielke, M.V. Universal Monos in Partial Morphism Categories. Appl Categor Struct 17, 435–444 (2009). https://doi.org/10.1007/s10485-007-9123-2

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  • DOI: https://doi.org/10.1007/s10485-007-9123-2

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