Eric Forgy Kan Extension

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Idea

The Kan extension of a functor $F : C \to D$ with respect to a functor

\array{ C \\ \downarrow^p \\ C' }

is, if it exists, a “best approximation” to the problem of finding a functor $C' \to D$ such that

\array{ C &\stackrel{F}{\to}& D \\ \downarrow^p & \nearrow \\ C' } \,,

i.e. to extending the domain of $F$ through $p$ from $C$ to $C'$ .

Kan extension may also be thought of as a generalization of left and right inverses.

Revised on June 18, 2009 at 20:42:57 by Eric Forgy