isIsomorphicTo
P29599
predicate
Indicates that two structures have a one-to-one, structure-preserving correspondence between their elements, making them equivalent in form even if not identical in content.
All labels observed (15)
| Label | Occurrences |
|---|---|
| isIsomorphicTo canonical | 27 |
| isomorphicTo | 18 |
| yieldsIsomorphism | 4 |
| givesIsomorphismBetween | 3 |
| hasCenterIsomorphicTo | 3 |
| centerIsIsomorphicTo | 2 |
| describesAsIsomorphic | 2 |
| expressesAsIsomorphism | 2 |
| groupIsIsomorphicTo | 2 |
| assertsIsomorphism | 1 |
| centerIsomorphicTo | 1 |
| hasComparisonIsomorphismWith | 1 |
| hasIsomorphism | 1 |
| isIsomorphicOverAlgebraicClosureTo | 1 |
| isomorphismType | 1 |
Description generation (PDg)
The one-sentence description above was generated by prompting gpt-5.1 with the predicate name and this instruction.
Instruction
Given a predicate that represents a relationship or action between entities, generate a one-sentence description explaining its meaning. # Instructions Focus on describing the relationship, not the entities themselves. # Response Format Begin the description with \' Indicates...\'
Input
Predicate: isIsomorphicTo
Generated description
Indicates that two structures have a one-to-one, structure-preserving correspondence between their elements, making them equivalent in form even if not identical in content.
Sample triples (69)
| Subject | Object |
|---|---|
| Brauer group | H^2(Gal(K^sep/K), (K^sep)^×) for a field K with separable closure K^sep via predicate surface "hasIsomorphism" ⓘ |
|
Jacobian varieties
surface form:
Jacobian variety
|
Picard variety of degree zero via predicate surface "isomorphicTo" NERFINISHED ⓘ |
|
Jacobian varieties
surface form:
Jacobian variety
|
Pic^0(C) via predicate surface "isomorphicTo" NERFINISHED ⓘ |
| Siegel upper half-space | Sp(2g,R)/U(g) as a symmetric space via predicate surface "isomorphicTo" ⓘ |
| Bott periodicity | π_{k}(U) ≅ π_{k+2}(U) via predicate surface "yieldsIsomorphism" ⓘ |
| Bott periodicity | π_{k}(O) ≅ π_{k+8}(O) via predicate surface "yieldsIsomorphism" ⓘ |
| Bott periodicity | K^{n}(X) ≅ K^{n+2}(X) for complex K-theory via predicate surface "yieldsIsomorphism" ⓘ |
| Bott periodicity | KO^{n}(X) ≅ KO^{n+8}(X) for real K-theory via predicate surface "yieldsIsomorphism" ⓘ |
| Tate curve | G_m / q^Z as rigid analytic groups ⓘ |
|
Möbius transformations
surface form:
Möbius transformation
|
PSL(2,ℂ) via predicate surface "groupIsIsomorphicTo" NERFINISHED ⓘ |
|
Möbius transformations
surface form:
Möbius transformation
|
PGL(2,ℂ) via predicate surface "groupIsIsomorphicTo" NERFINISHED ⓘ |
|
PSL(2,\mathbb{C})
surface form:
PSL(2,ℂ)
|
group of orientation-preserving isometries of hyperbolic 3-space ⓘ |
|
PSL(2,\mathbb{C})
surface form:
PSL(2,ℂ)
|
Isom⁺(ℍ³) ⓘ |
|
PSL(2,\mathbb{C})
surface form:
PSL(2,ℂ)
|
PGL(2,ℂ) NERFINISHED ⓘ |
| SL(2,7) | C2 via predicate surface "centerIsIsomorphicTo" ⓘ |
| SL(2,7) | 2·PSL(2,7) NERFINISHED ⓘ |
| PGL(2,7) | PGL(2,7) via predicate surface "isomorphicTo" NERFINISHED ⓘ |
| PGL(2,7) | PΓL(2,7) via predicate surface "isomorphicTo" NERFINISHED ⓘ |
| S5 | group of all bijections on a 5-element set ⓘ |