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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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