# Definition:Category of Relations

## 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.