Editing Kernel (category theory) (section)

{{short description|Generalization of the kernel of a homomorphism}}
{{other uses|Kernel (disambiguation)}}

{{More citations needed|date=December 2009}}
In [[category theory]] and its applications to other branches of [[mathematics]], '''kernels''' are a generalization of the kernels of [[group homomorphism]]s, the kernels of [[module homomorphism]]s and certain other [[kernel (algebra)|kernels from algebra]]. Intuitively, the kernel of the [[morphism]] ''f'' : ''X'' → ''Y'' is the "most general" morphism ''k'' : ''K'' → ''X'' that yields zero when composed with (followed by) ''f''.

Note that [[kernel pair]]s and [[difference kernel]]s (also known as binary [[Equaliser (mathematics)|equaliser]]s) sometimes go by the name "kernel"; while related, these aren't quite the same thing and are not discussed in this article.