Statements (20)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
Category theory concept |
| gptkbp:appearsIn |
Abelian category
Additive category |
| gptkbp:definedIn |
Morphism
|
| gptkbp:field |
Category theory
|
| gptkbp:formalDefinition |
Given a morphism f:X→Y, a kernel is a morphism k:K→X such that f∘k=0 and for any morphism k':K'→X with f∘k'=0, there exists a unique u:K'→K with k∘u=k'.
|
| gptkbp:generalizes |
gptkb:Kernel_(algebra)
|
| gptkbp:hasDual |
Cokernel (category theory)
|
| gptkbp:hasProperty |
Universal property
|
| gptkbp:hasWikipediaPage |
https://en.wikipedia.org/wiki/Kernel_(category_theory)
|
| https://www.w3.org/2000/01/rdf-schema#label |
Kernel (category theory)
|
| gptkbp:isFunctorial |
Yes
|
| gptkbp:relatedTo |
Abelian category
Morphism Cokernel (category theory) |
| gptkbp:usedIn |
Homological algebra
Exact sequence |
| gptkbp:bfsParent |
gptkb:Kernel_(algebra)
|
| gptkbp:bfsLayer |
8
|