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:<math>\hom_\mathcal C((R,S), \mathcal F(T,U))\to \hom_\mathcal D ((S^{-1}R, j(S)), (T,U)).</math>
This may seem a rather tricky way of expressing the universal property, but it is useful for showing easily many properties, by using the fact that the composition of two left adjoint functors is a left adjoint functor.
=== Examples ===
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