Initial and final compared (category theory)

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This page shows Initial and Final side by side, for more details on each see their respective pages.
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Let [ilmath]\mathcal{C} [/ilmath] be a category and let [ilmath]S\in\text{Ob}(\mathcal{C})[/ilmath], then we say [ilmath]S[/ilmath] is:

Initial[1] Final[1]
if for each [ilmath]A\in\text{Ob}(\mathcal{C})[/ilmath] there exists a unique morphism:
[ilmath]\xymatrix{S \ar[r] & A} [/ilmath] [ilmath]\xymatrix{A \ar[r] & S} [/ilmath]


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