In this talk 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 between Gromov-Witten 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.