Constant diagram functor
= Constant diagram functor
{title2=$\Delta_J:\mathcal C\to[J,\mathcal C]$}
The constant diagram functor sends $C$ to the <functor> on $J$ with constant object value $C$ and identity arrow values; a morphism $f$ becomes the <natural transformation> with every component $f$. When all $J$-shaped <categorical limits> exist, it is a <left adjoint> to the <limit functor>.