- 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...
-
injective non-
surjective function (injection, not a bijection) An
injective surjective function (bijection) A non-injective
surjective function (surjection...
- 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...
-
epimorphism (
surjective) ⟹
epimorphism (right cancelable) ; {\displaystyle {\text{split epimorphism}}\implies {\text{epimorphism (
surjective)}}\implies...
-
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 ) =...
-
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...
-
categorical analogues of onto or
surjective functions (and in the
category of sets the
concept corresponds exactly to the
surjective functions), but they may...
- In
functional analysis, a
unitary operator is a
surjective bounded operator on a
Hilbert space that
preserves the
inner product.
Unitary operators are...
