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Cover Relations on Categories

Applied Categorical Structures volume 17, pages 351–371 (2009)Cite this article

Abstract

A cover relation on a category ℂ is a binary relation ⊏ on the class of morphisms of ℂ, which is defined only for those pairs of morphisms which have the same codomain, and which has the following two properties: (i) if f ⊏ g and h is composable with f, then hf ⊏ hg, (ii) if f ⊏ g and f is composable with e then fe ⊏ g. We study cover relations arising from a special type of factorization systems, and cover relations arising from a special type of monoidal structures.

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Authors and Affiliations

  1. Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, Cape Town, South Africa

    Zurab Janelidze

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  1. Zurab Janelidze
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Correspondence to Zurab Janelidze.

Additional information

Supported by Claude Leon Foundation, INTAS (06-1000017-8609) and Georgian National Science Foundation (GNSF/ST06/3-004).

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Janelidze, Z. Cover Relations on Categories. Appl Categor Struct 17, 351–371 (2009). https://doi.org/10.1007/s10485-008-9134-7

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  • DOI: https://doi.org/10.1007/s10485-008-9134-7

Keywords

  • Cover relation
  • Factorization system
  • Monoidal category

Mathematics Subject Classifications (2000)

  • 18A32
  • 18D10