Final object

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Definition

Definition with symbols

An object $A$ in a category ${\mathcal {C}}$ is termed a final object if for every object $B\in {\mathcal {C}}$, there is a unique morphism from $B$ to $A$.

If a final object exists, then any two final objects are isomorphic, and there is a unique isomorphism between any two final objects. In particular, the automorphism group of a final object is trivial.

Related notions

• Initial object
• Zero object