universalProperty
P77813
predicate
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 | every continuous map from the original space to a compact space sending points escaping to infinity to a single point factors uniquely through it ⓘ |
| Alexandrov compactification | minimal compactification adding only one point ⓘ |
| 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 ⓘ |
| 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 ⓘ |
|
Jacobian varieties
surface form:
Jacobian variety
|
universal abelian variety receiving a map from the curve ⓘ |
|
Jacobian varieties
surface form:
Jacobian variety
|
universal regular quotient of degree-zero divisors ⓘ |
| Stone–Čech compactification | every continuous map from X to a compact Hausdorff space factors uniquely through βX ⓘ |
| Verma module | initial object among highest-weight modules with fixed highest weight ⓘ |
|
universal enveloping algebras
surface form:
universal enveloping algebra
|
every Lie algebra homomorphism into the Lie algebra of an associative algebra factors uniquely through it ⓘ |