  We reframe a collection of well-known comparison results in genus zero
Gromov-Witten theory in order to relate these to integral transforms between
derived categories. This implies that various comparisons among Gromov-Witten
theories and FJRW theory are compatible with the integral structure introduced
by Iritani. We conclude with a proof that a version of the LG/CY correspondence
relating quantum D-modules with Orlov's equivalence is implied by a version of
the crepant transformation conjecture.
