In mathematics, a corestriction[1] of a function is a notion analogous to the notion of a restriction of a function.
The duality prefix co- here denotes that while the restriction changes the domain to a subset, the corestriction changes the codomain to a subset.
However, the notions are not categorically dual.
we can consider the corresponding inclusion of sets
Then for any function
of a function
can be defined as the composition
Analogously, for an inclusion
the corestriction
is the unique function
The corestriction exists if and only if
In particular, the corestriction onto the image always exists and it is sometimes simply called the corestriction of
More generally, one can consider corestriction of a morphism in general categories with images.
[2] The term is well known in category theory, while rarely used in print.
[3] Andreotti[4] introduces the above notion under the name coastriction, while the name corestriction reserves to the notion categorically dual to the notion of a restriction.
is a surjection of sets (that is a quotient map) then Andreotti considers the composition
, which surely always exists.