 Since the structure in any of these definitions gives rise to the structures in the others, switching between them makes implicit use of a great deal of tedious details that would otherwise have to be repeated separately in every subject area.The theory of adjoints has the terms "left" and "right" at its foundation, and there are many components which live in one of two categories "C" and "D" which are under consideration.Therefore it can be helpful to choose letters in alphabetical order according to whether they live in the "lefthand" category "C" or the "righthand" category "D", and also to write them down in this order whenever possible.