Statements (50)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:canBe |
infinite
finite unbounded bounded |
| gptkbp:category |
category of chain complexes
|
| gptkbp:component |
gptkb:C_n
d_n |
| gptkbp:consistsOf |
sequence of abelian groups
sequence of modules |
| gptkbp:dualObject |
cochain complex
|
| gptkbp:field |
gptkb:topology
homological algebra |
| gptkbp:generalizes |
exact sequence
|
| gptkbp:hasApplication |
gptkb:algebraic_K-theory
gptkb:category_theory gptkb:de_Rham_cohomology group cohomology sheaf cohomology simplicial homology spectral sequences singular homology derived functors |
| gptkbp:hasGrading |
integer grading
|
| gptkbp:hasInvariant |
homology group
|
| gptkbp:homotopy |
chain homotopy
|
| https://www.w3.org/2000/01/rdf-schema#label |
Chain complex
|
| gptkbp:morphism |
chain map
|
| gptkbp:notation |
(C_n, d_n)
|
| gptkbp:originatedIn |
algebraic structures
categories modules vector spaces differential forms rings simplicial complexes topological spaces functors algebras group actions sheaves cellular complexes |
| gptkbp:property |
composition of consecutive boundary maps is zero
|
| gptkbp:relatedTo |
differential graded algebra
cochain complex |
| gptkbp:structure |
boundary maps
|
| gptkbp:usedIn |
definition of cohomology
definition of homology |
| gptkbp:bfsParent |
gptkb:Cohomology_group
|
| gptkbp:bfsLayer |
7
|