In algebraic geometry, a Fourier–Mukai transform ΦK  is a functor between derived categories of coherent sheaves D(X) → D(Y) for schemes X and Y, which is, in a sense, an integral transform along a kernel object K ∈ D(X×Y).
In algebraic geometry, the Fourier–Mukai transform ΦK is a correspondence between the categories of coherent sheaves on two schemes X and Y, which shares similarities with the concept of an integral transformation along a kernel object K in the derived category of the product scheme X×Y.