, the notion of restriction
finds a general definition in the context of sheaves
Often, the following definition will be sufficient:
If f: E -> F is a (partial) function from E to F, and A is a subset of E, then the restriction of f to A is the (partial) function
- having the graph .
(In rough words, it is "the same function", but only defined on .)
More generally, the restriction of a binary relation is usually defined in the same way. (One could also define a restriction to a subset of E x F, and the same applies to n-ary relations.
These cases do not fit into the scheme of sheaves.)
- The restriction of the non injective function to is the injection .
- The canonical injection of a set A into a superset E of A.