Definition:Category of Relations

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Definition

The category of (binary) relations, denoted $\mathbf{Rel}$, is the metacategory with:

Objects:         sets
Morphisms: binary relations $\mathcal R \subseteq A \times B$.
Composition: composition of relations
Identity morphisms: identity mappings


Note

The reason to call $\mathbf{Rel}$ a metacategory is foundational; allowing it to be a category would bring us to axiomatic troubles.


Also see


Sources