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Date: 11-7-2021
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Date: 9-6-2021
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Date: 10-8-2021
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Let be a function defined on a set
and taking values in a set
. Then
is said to be a surjection (or surjective map) if, for any
, there exists an
for which
. A surjection is sometimes referred to as being "onto."
Let the function be an operator which maps points in the domain to every point in the range and let be a vector space with
. Then a transformation
defined on
is a surjection if there is an
such that
for all
.
In the categories of sets, groups, modules, etc., an epimorphism is the same as a surjection, and is used synonymously with "surjection" outside of category theory.
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