Category of Functors

If \(\C\) is small (\(\hom{\C}\) is a set). All functors from \(\C\) to some category \(\D\) form the category \(\mathrm{Func}(\C,\D)\).

• \(\ob{\mathrm{Func}(\C,\D)}\): Functors \(F:\C→\D\)
• \(\hom{\mathrm{Func}(\C,\D)}\): natural transformations
• ∘: Functor composition

\(\mathrm{Func}(\C,\C)\) is the category of endofunctors of \(\C\).