Colimit-preserving functor
= Colimit-preserving functor
Relative to a specified class of diagram shapes, a functor preserves colimits when it takes each existing <colimit> cocone of those shapes to a <colimit> cocone. A <left adjoint> preserves all existing colimits, including large ones when their universal properties are meaningful. Small-colimit preservation alone does not imply preservation of a class-indexed colimit.