  C-systems were introduced by J. Cartmell under the name "contextual
categories". In this note we study sub-objects and quotient-objects of
C-systems. In the case of the sub-objects we consider all sub-objects while in
the case of the quotient-objects only {\em regular} quotients that in
particular have the property that the corresponding projection morphism is
surjective both on objects and on morphisms.
  It is one of several short papers based on the material of the "Notes on Type
Systems" by the same author. This version is essentially identical with the
version published in Contemporary Mathematics n.658.
