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