Limit functor
= Limit functor
{title2=$\lim_J:[J,\mathcal C]\to\mathcal C$}
With chosen $J$-shaped <categorical limits>, the limit functor sends each <diagram in a category> to its limit object. A <natural transformation> induces the unique morphism compatible with the limit-cone projections. It is a <right adjoint> to the <constant diagram functor>, so it preserves existing <categorical limits>.