Definition:Unique up to Unique Isomorphism

Definition

Let $\mathbf C$ be a category.

Let $S \subseteq \operatorname{Ob}(\mathbf C)$ be a subclass of its objects.

The class $S$ is unique up to unique isomorphism if and only if for all objects $s,t \in S$ there is a unique isomorphism from $s$ to $t$.

Also see

Weaker properties

• Definition:Unique up to Isomorphism

Stronger properties

• Definition:Unique up to Unique Morphism, as shown at Unique up to Unique Morphism implies Unique up to Unique Isomorphism