Embedding is the morphism $( A ; B ; \operatorname{id}_A)$ of the category $\mathbf{Rel}$ for sets $A \subseteq B$.
I call restriction the morphism $( A ; B ; \operatorname{id}_B)$ for sets $A \supseteq B$.
For embedding there is a standard notation: $A \hookrightarrow B$.
Is there a standard notation (and/or terminology) for restriction?
Moreover, is there a notation for $( A ; B ; \operatorname{id}_{A \cap B})$ which generalizes both embedding and restriction?