An important property of adjoint pairs is that they restrict to equivalences on subcategories, and this is what we get in the Galois theory and algebraic geometry examples above: the first adjoint pair is an equivalence by the fundamental theorem of Galois theory, and the second adjoint pair restricts to an equivalence ...

Are adjoint functors unique?

adjoint functors are, if they exist, unique up to natural isomorphism, this is Prop. 2.1 below; the concept of adjoint functors makes sense also relative to a full subcategory on which representing objects exists, this is the content of Remark 1.7 below.

What is an Adjunction category theory?

In mathematics, specifically category theory, adjunction is a relationship that two functors may have. Two functors that stand in this relationship are known as adjoint functors, one being the left adjoint and the other the right adjoint.