Definition:Unique up to Unique Isomorphism

Definition

Let $\mathbf C$ be a category.

Let $S \subseteq \map {\operatorname {Ob} } {\mathbf C}$ 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 exists 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

Sources

There are no source works cited for this page. Source citations are highly desirable, and mandatory for all definition pages. Definition pages whose content is wholly or partly unsourced are in danger of having such content deleted. To discuss this page in more detail, feel free to use the talk page.