universalProperty
P77813
predicate
Indicates that a property or characteristic holds for all members of a specified set or domain without exception.
All labels observed (1)
| Label | Occurrences |
|---|---|
| universalProperty canonical | 11 |
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: universalProperty
Generated description
Indicates that a property or characteristic holds for all members of a specified set or domain without exception.
Sample triples (11)
| Subject | Object |
|---|---|
| Alexandrov compactification | minimal compactification adding only one point ⓘ |
| Alexandrov compactification | every continuous map from the original space to a compact space sending points escaping to infinity to a single point factors uniquely through it ⓘ |
| Grothendieck group | every monoid homomorphism to an abelian group factors uniquely through it ⓘ |
| Henselization | any local homomorphism from the original ring to a Henselian local ring factors uniquely through its Henselization ⓘ |
|
universal enveloping algebra
linked to:
universal enveloping algebras
|
every Lie algebra homomorphism into the Lie algebra of an associative algebra factors uniquely through it ⓘ |
| Verma module | initial object among highest-weight modules with fixed highest weight ⓘ |
| Stone–Čech compactification | every continuous map from X to a compact Hausdorff space factors uniquely through βX ⓘ |
| Cauchy completion | every uniformly continuous map from the original space to a complete metric space extends uniquely ⓘ |
| Cauchy completion | initial object among complete metric spaces receiving an isometric embedding of the original space ⓘ |
|
Jacobian variety
linked to:
Jacobian varieties
|
universal regular quotient of degree-zero divisors ⓘ |
|
Jacobian variety
linked to:
Jacobian varieties
|
universal abelian variety receiving a map from the curve ⓘ |