Note that denotes the identify functor on the category , denotes the identity natural transformation from the functor to itself, and denotes the identity morphism of the object thumb|String diagram for adjunction. These equations are useful in reducing proofs about adjoint functors to algebraic manipulations. They are sometimes called the triangle identities, or sometimes the zig-zag equations because of the appearance of the corresponding string diagrams. A way to remember them is to first write down the nonsensical equation and then fill in either or in one of the two simple ways that make the compositions defined.
Note that denotes the identify functor on the category , denotes the identity natural transformation from the functor to itself and denotes the identity morphism of the object thumb|String diagram for adjunction. These equations are useful in reducing proofs about adjoint functors to algebraic manipulations. They are sometimes called the triangle identities, or sometimes the zig-zag equations because of the appearance of the corresponding string diagrams. A way to remember them is to first write down the nonsensical equation and then fill in either or in one of the two simple ways that make the compositions defined.