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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 fg and h is composable with f, then hfhg, (ii) if fg and f is composable with e then feg. 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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Correspondence to Zurab Janelidze.

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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).

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Mathematics Subject Classifications (2000)