Formal criteria for adjoint functors

In category theory, a branch of mathematics, the formal criteria for adjoint functors are criteria for the existence of a left or right adjoint of a given functor.
One criterion is the following, which first appeared in Peter J. Freyd's 1964 book "Abelian Categories, an Introduction to the Theory of Functors":
Another criterion is:
)</math> exists in formula_1.
Moreover, when this is the case then a left adjoint of "G" can be computed using the left Kan extension.