Definition:Category of Relations

From ProofWiki
Jump to navigation Jump to search


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


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

Also see