Editing Adjoint functors (section)

===Conventions===

The theory of adjoints has the terms ''left'' and ''right'' at its foundation, and there are many components that live in one of two categories ''C'' and ''D'' that 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.

In this article for example, the letters ''X'', ''F'', ''f'', ε will consistently denote things that live in the category ''C'', the letters ''Y'', ''G'', ''g'', η will consistently denote things that live in the category ''D'', and whenever possible such things will be referred to in order from left to right (a functor ''F'' : ''D'' → ''C'' can be thought of as "living" where its outputs are, in ''C''). If the arrows for the left adjoint functor F were drawn they would be pointing to the left; if the arrows for the right adjoint functor G were drawn they would be pointing to the right.