We introduce multiplicative
Dirac structures on Lie groupoids, providing a unified framework to study both
multiplicative Poisson bivectors (Poisson groupoids) and multiplicative closed 2-forms
such as symplectic groupoids. We prove that for every source simply connected Lie
groupoid G with Lie algebroid AG, there exists a one-to-one correspondence between
multiplicative Dirac structures on G and Dirac structures on AG that are compatible
with both the linear and algebroid structures of AG. We explain in what sense this
extends the integration of Lie bialgebroids to Poisson groupoids and the
integration of Dirac manifolds. We explain the connection between multiplicative
Dirac structures and higher geometric structures such as ℒ𝒜-groupoids and
𝒞𝒜-groupoids.
