  We study the meaning of "adding a constant to a language" for any doctrine,
and "adding an axiom to a theory" for a primary doctrine, by showing how these
are actually two instances of the same construction. We prove their universal
properties, and how these constructions are compatible with additional
structure on the doctrine. Existence of Kleisli object for comonads in the
2-category of indexed poset is proved in order to build these constructions.
