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 $\{*\}\xrightarrow{d}D$ is a final functor as defined here.

单词	Final functor
释义	Final functor 英语百科 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 $\{*\}\xrightarrow{d}D$ is a final functor as defined here.
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