Category theory MOC

Kernel

In a category 𝖢 with zero morphisms, the kernel ker⁡𝑓 of a morphism 𝑓 ∈𝖢(𝑋,𝑌) is the equalizer of 𝑓 with the zero morphism 0 ∈𝖢(𝑋,𝑌). cat

The dual notion is the cokernel.

Examples in particular categories

• Kernel of a group homomorphism in Category of groups and Category of abelian groups
• Linear kernel in Category of vector spaces
• Module kernel in Category of left modules
• Kernel of an algebra homomorphism in Category of algebras
• Kernel of a Lie algebra homomorphism in Category of Lie algebras

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