cohomology theory
C22356
concept
A cohomology theory is a functorial assignment of graded algebraic invariants to topological spaces (or other mathematical objects) that encodes global structural and obstruction information via axioms such as exactness and homotopy invariance.
All labels observed (7)
| Label | Occurrences |
|---|---|
| cohomology theory canonical | 11 |
| branch of algebraic topology | 1 |
| cobordism theory | 1 |
| differential cohomology theory | 1 |
| generalized cohomology invariant | 1 |
| generalized cohomology theory | 1 |
| refined cohomology theory | 1 |
Description generation (CDg)
The one-sentence description above was generated by prompting gpt-5.1 with the class name and this instruction.
Instruction
generate a one-sentence description for a given conceptual class. # Response Format Return only the sentence: "Description: [one-sentence description of the conceptional class]"
Input
Class: cohomology theory
Generated description
A cohomology theory is a functorial assignment of graded algebraic invariants to topological spaces (or other mathematical objects) that encodes global structural and obstruction information via axioms such as exactness and homotopy invariance.
Instances (14)
| Instance | Via concept surface |
|---|---|
| Alexandrov–Čech cohomology | — |
| Weil cohomology | — |
| étale cohomology | — |
| K-theory | — |
|
Galois cohomology
linked to:
Galois
|
— |
| Deligne cohomology | — |
| de Rham cohomology | — |
| Hirzebruch genera | generalized cohomology invariant |
| Thom cobordism theory | branch of algebraic topology |
| Alexander–Spanier cohomology | — |
| Galois cohomology | — |
| Tate cohomology | — |
| Chow groups | — |
| Cheeger–Simons differential characters | differential cohomology theory |