Maths - Category Theory - Weak Equivilance

Weak equivilance provides a simpler way to determine equivilance.

On the equivilance page we discussed how to determine equivilance by finding two functors. F and G, which give the identity when composed in both directions. equivilance
Weak equivilance gives us a way to do this using only a functor in one direction F. However this only tells us that an equivilance exists, not the functors which give the equivilance. weak equivilance

Given this functor F : C -> D there is an equivalence if and only if the following are all true:

Further Information

Weak equivalence was first used in algebraic topology, in particular, in model category theory as described on the page here.

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see also:

Adjunctions from Morphisms

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