Eric Forgy Kan Extension

Idea

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

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

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

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

i.e. to extending the domain of FF through pp from CC to CC'.

Relation to Left and Right Inverses

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