Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Functor
|
| gptkbp:appearsIn |
gptkb:Serre–Swan_theorem
gptkb:Atiyah–Hirzebruch_spectral_sequence |
| gptkbp:assigns_to_a_ring |
gptkb:Grothendieck_group_of_finitely_generated_projective_modules
|
| gptkbp:capturedBy |
direct sum structure of modules
isomorphism classes of projective modules |
| gptkbp:category-theoretic_context |
abelian categories
exact categories |
| gptkbp:field |
gptkb:algebraic_K-theory
|
| gptkbp:generalizes |
gptkb:Grothendieck_group
|
| https://www.w3.org/2000/01/rdf-schema#label |
K 0 functor
|
| gptkbp:importantFor |
classification of vector bundles
classification of projective modules |
| gptkbp:introduced |
gptkb:Alexander_Grothendieck
|
| gptkbp:maps_from |
category of rings
|
| gptkbp:maps_to |
abelian groups
|
| gptkbp:notation |
K_0(R) for a ring R
|
| gptkbp:relatedTo |
gptkb:higher_K-functors
|
| gptkbp:used_in |
gptkb:algebraic_geometry
gptkb:topology operator algebras |
| gptkbp:bfsParent |
gptkb:Grothendieck_group
|
| gptkbp:bfsLayer |
6
|