Final functor

In category theory, the notion of final functor (resp. initial functor) is a generalization of the notion of final object (resp. initial object) in a category.

A functor $F:C\to D$ is called final if, for any set-valued functor $G:D\to \mathbf{\text{𝐒𝐞𝐭}}$, the colimit of G is the same as the colimit of $G\circ F$. Note that an object d ∈ Ob(D) is a final object in the usual sense if and only if the functor $\{*\}\stackrel{d}{\to }D$ is a final functor as defined here.

The notion of initial functor is defined as above, replacing final by initial and colimit by limit.

References

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External links

• http://ncatlab.org/nlab/show/final+functor