Essential geometric morphism
= Essential geometric morphism
{title2=$f_!\dashv f^*\dashv f_*$}
A <geometric morphism> is essential when its inverse image has an additional <left adjoint>. For a <functor> of small categories, precomposition on presheaves has <left Kan extension> and <Right Kan extension> as its two adjoints. Precomposition preserves <finite limits> pointwise, so this is an essential <geometric morphism>.