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Category of relations — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Category_of_relations
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-07T14:40:34.798Z
SHA-256 of the archived text: 83c26372e186f9732b021bcfbf33909c45240623f3910c53ae81f439e848ce10
Stable URL of this page: https://metraipolis.com/documento/dc_4e65625b8a67

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Category of relations — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Category_of_relations (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_4e65625b8a67 (Metraipolis archive dc_4e65625b8a67, sha256 83c26372e186f9732b021bcfbf33909c45240623f3910c53ae81f439e848ce10)

BibTeX

@misc{dc4e65625b8a67,
  title = {Category of relations — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Category_of_relations},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_4e65625b8a67; sha256 83c26372e186f9732b021bcfbf33909c45240623f3910c53ae81f439e848ce10},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Category_of_relations. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In mathematics, the category Rel has the class of sets as objects and binary relations as morphisms. A morphism (or arrow) R : A → B in this category is a relation between the sets A and B, so R ⊆ A × B. The composition of two relations R: A → B and S: B → C is given by ( a , c ) ∈ S ∘ R ⟺ for some b ∈ B , ( a , b ) ∈ R and ( b , c ) ∈ S . {\displaystyle (a,c)\in S\circ R\iff {\text{for some }}b\in B,(a,b)\in R{\text{ and }}(b,c)\in S.} Rel has also been called the "category of correspondences of sets".

Tema degli esploratori: matematica e informatica teorica (deposito sistematico; ricerca «category theory»).
Fonte: Wikipedia in inglese, voce «Category of relations» — https://en.wikipedia.org/wiki/Category_of_relations
Wikidata Q5051849 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q5051849
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Category_of_relations?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1371089161, consultata il 2026-10-07T14:14:14.455Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: 2dda2dd881f0c295c5239be36d22503af0a9ad27ffa852ff3ed26e5f25ba1c8b