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 $G: D\to Set$, 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 Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): \{*\}\xrightarrow{d}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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See also

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