More precisely, finite limits are contained in the saturation of the class containing only finite products and equalizers, and also that of the class containing only pullbacks and terminal objects. (The actual saturation is somewhat larger than this — it is the class of L-finite limits.)

A functor that preserves finite limits is called left exact functor, a lex functor, a cartesian functor, or a finitely continuous functor. The 2-category of finitely complete categories, left exact functors and natural transformations is called Lex.