  In this work we introduce the category of multiplicative sections of an
$\la$-groupoid. We prove that this category carries natural strict Lie
2-algebra structures, which are Morita invariant. As applications, we study the
algebraic structure underlying multiplicative vector fields on a Lie groupoid
and in particular vector fields on differentiable stacks. We also introduce the
notion of geometric vector field on the quotient stack of a Lie groupoid,
showing that the space of such vector fields is a Lie algebra. We describe the
Lie algebra of geometric vector fields in several cases, including classifying
stacks, quotient stacks of regular Lie groupoids and in particular orbifolds,
and foliation groupoids.
