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). #m/def/cat

The dual notion is the cokernel.

Examples in particular categories

• Kernel of a group homomorphism in 𝖦𝗋𝗉 and 𝖠𝖻
• Linear kernel in 𝖵𝖾𝖼𝗍𝕂
• Module kernel in 𝑅𝖬𝗈𝖽
• Kernel of an algebra homomorphism in 𝖠𝗅𝗀𝕂
• Kernel of a Lie algebra homomorphism in 𝖫𝗂𝖾𝕂

#state/tidy | #lang/en | #SemBr