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The free cocompletion. A lot of adjoint couple couples of functors are just particular case of this construction, and often it is easier to use the general theorem than working out a particular case by hand (for example for $i_{!}$ and $i^{!}$).

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The free cocompletion. A lot of adjoint couple of functors are just particular case of this construction, and often it is easier to use the general theorem than working out a particular case by hand (for example for $i_{!}$ and $i^{!}$).