 an adjunction whose unit and counit are isomorphisms.Every adjunction 〈"F", "G", ε, η〉 extends an equivalence of certain subcategories.Define "C"1 as the full subcategory of "C" consisting of those objects "X" of "C" for which ε"X" is an isomorphism, and define "D"1 as the full subcategory of "D" consisting of those objects "Y" of "D" for which η"Y" is an isomorphism.