- In mathematics, a
surjective function (also
known as surjection, or onto
function /ˈɒn.tuː/) is a
function f such that, for
every element y of the function's...
- {\displaystyle \forall x,x'\in X,x\neq x'\implies f(x)\neq f(x').} The
function is
surjective, or onto, if each
element of the
codomain is
mapped to by at
least one...
-
category theory, a
functor F:C→D{\displaystyle F:C\to D} is
essentially surjective if each
object d{\displaystyle d} of D{\displaystyle D} is isomorphic...
-
epimorphism (
surjective) ⟹
epimorphism (right cancelable) ; {\displaystyle {\text{split epimorphism}}\implies {\text{epimorphism (
surjective)}}\implies...
- In
category theory, a point-
surjective morphism is a
morphism f : X → Y {\displaystyle f:X\rightarrow Y} that "behaves" like
surjections on the category...
-
injective non-
surjective function (injection, not a bijection) An
injective surjective function (bijection) A non-injective
surjective function (surjection...
-
injective non-
surjective function (injection, not a bijection) An
injective surjective function (bijection) A non-injective
surjective function (surjection...
- other, and so each b in X may
occur at most once in the
image of f. f is
surjective: for each b in X
there must be at
least one a in N such that f(a)=b{\displaystyle...
-
function are the same set; such a
function is
called surjective or onto. For any non-
surjective function f:X→Y,{\displaystyle f:X\to Y,} the codomain...
- 1 ( y ) = { x } . {\displaystyle f^{-1}(y)=\{x\}.} The
function f is
surjective (or onto, or is a surjection) if its
range f ( X ) {\displaystyle f(X)}...
