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Definition: Lift

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In mathematics, given the morphisms f:Xf: XYY and g:Yg: YZZ, a lift of ff to ZZ is a morphism h:Xh: XZZ such that ff = g(h)g(h).

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The basic idea involves two objects, XX and YY, that interact intuitively (as required) and make​ it easy to define a good morphism (f:Xf: XYY). Then, there exists another object, ZZ, that easily relates to YY (morphism g:Yg: YZZ), but it’s not explicit in how it relates to XX.

In this case, the morphism gg will be used to lift ff to ZZ using gg. A new morphism (h:Xh: XZZ) will be determined where ff = g(h)g(h).

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