mathematical structure
C3748
concept
A mathematical structure is a set (or collection of objects) equipped with specified operations, relations, or properties that satisfy given axioms, providing a framework for studying abstract patterns and relationships.
All labels observed (48)
| Label | Occurrences |
|---|---|
| mathematical theory | 56 |
| Lie group | 24 |
| algebraic structure | 21 |
| mathematical group | 16 |
| mathematical structure canonical | 15 |
| integer sequence | 13 |
| topological space | 12 |
| mathematical framework | 9 |
| finite group | 8 |
| associative algebra | 7 |
| non-abelian group | 6 |
| combinatorial structure | 4 |
| dimension theory concept | 4 |
| symmetry group | 3 |
| category-theoretic structure | 2 |
| causal structure representation | 2 |
| formal logical system | 2 |
| metric space | 2 |
| noncommutative algebra | 2 |
| number system | 2 |
| ordered field | 2 |
| stability theory | 2 |
| structure in Hodge theory | 2 |
| structure in differential geometry | 2 |
| *-algebra | 1 |
| Steiner system | 1 |
| algebraic framework | 1 |
| categorical structure | 1 |
| concept in convex analysis | 1 |
| concept in discrete mathematics | 1 |
| construction in partition theory | 1 |
| fixed-point theory | 1 |
| group theory construction | 1 |
| information geometric structure | 1 |
| mathematical field | 1 |
| mathematical notion | 1 |
| mathematical structure in general relativity | 1 |
| model-theoretic construct | 1 |
| order-theoretic concept | 1 |
| order-theoretic structure | 1 |
| second-order logical system | 1 |
| set of mathematical conditions | 1 |
| set-theoretic construct | 1 |
| set-theoretic universe | 1 |
| structure in algebraic geometry | 1 |
| structure in classical field theory | 1 |
| structure in classical mechanics | 1 |
| unique factorization domain | 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: mathematical structure
Generated description
A mathematical structure is a set (or collection of objects) equipped with specified operations, relations, or properties that satisfy given axioms, providing a framework for studying abstract patterns and relationships.
Instances (220)
| Instance | Via concept surface |
|---|---|
| Temperley–Lieb algebra | associative algebra |
| 4-sphere S^4 | topological space |
| Kirby calculus | mathematical theory |
| ADE singularity theory | mathematical theory |
| Floer theory | mathematical theory |
|
CW complexes
surface form:
CW complex
|
topological space |
| Picard–Lefschetz theory | mathematical theory |
| Quillen K-theory | mathematical theory |
| Bruhat–Tits theory | mathematical theory |
| Tits building | combinatorial structure |
|
mixed Hodge structures
surface form:
mixed Hodge structure
|
structure in Hodge theory |
| Marchenko theory | mathematical theory |
| Cartwright–Littlewood theory on nonlinear differential equations | mathematical theory |
| theory of regularity structures | mathematical theory |
| Gelfand–Tsetlin graph | combinatorial structure |
| Bernstein–Zelevinsky classification | mathematical theory |
| theory of D-modules | mathematical theory |
| Fox calculus | mathematical theory |
| Kripke frame | — |
| Grothendieck universe | set-theoretic construct |