Coherent functor
= Coherent functor
A <functor> between <coherent categories> is coherent when it preserves <finite limits>, image factorizations and finite unions of <subobjects>, including the empty union. It consequently preserves the interpretation of every <coherent formula>. A <coherent functor> from a <coherent syntactic category> to a <topos> is equivalent to a model of the corresponding <coherent theory>; <natural transformations> correspond to ordinary model homomorphisms.