Grothendieck group of a category
GPTKB entity
Statements (17)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
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| gptkbp:appliesTo |
abelian category
exact category |
| gptkbp:built |
The Grothendieck group is constructed by taking isomorphism classes of objects and imposing relations based on short exact sequences.
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| gptkbp:defines |
The Grothendieck group of a category is an abelian group constructed from the objects of a category, typically an exact or abelian category.
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| gptkbp:example |
The Grothendieck group of the category of finitely generated abelian groups is isomorphic to the integers.
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| https://www.w3.org/2000/01/rdf-schema#label |
Grothendieck group of a category
|
| gptkbp:namedAfter |
gptkb:Alexander_Grothendieck
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| gptkbp:notation |
K_0(C)
|
| gptkbp:property |
universal property with respect to additive functors
|
| gptkbp:relatedTo |
gptkb:K-theory
gptkb:Grothendieck_ring |
| gptkbp:usedIn |
gptkb:algebra
gptkb:algebraic_geometry gptkb:category_theory |
| gptkbp:bfsParent |
gptkb:K_0
|
| gptkbp:bfsLayer |
7
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