Final (category theory)

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See initial and final compared (category theory) for this definition and its dual side by side
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Created to move towards nets and generalised convergence/limits.
  • Demote once examples and co are added


Let [ilmath]\mathcal{C} [/ilmath] be a category and let [ilmath]S\in\text{Ob}(\mathcal{C})[/ilmath] be any object of [ilmath]\mathcal{C} [/ilmath]. Then [ilmath]S[/ilmath] is final (or terminal[1]) in [ilmath]\mathcal{C} [/ilmath] if[1]:

  • For all [ilmath]A\in\text{Ob}(\mathcal{C})[/ilmath]
    • there exists a unique morphism: [ilmath]\xymatrix{A \ar[r] & S} [/ilmath]


See also


  1. 1.0 1.1 An Introduction to Category Theory - Harold Simmons - 1st September 2010 edition