universalProperty

P77813

predicate

Indicates that a property or characteristic holds for all members of a specified set or domain without exception.

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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 ⓘ