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In this work we introduce the category of multiplicative sections of an$\la$-groupoid. We prove that this category carries natural strict Lie2-algebra structures, which are Morita invariant. As applications, we study thealgebraic structure underlying multiplicative vector fields on a Lie groupoidand in particular vector fields on differentiable stacks. We also introduce thenotion 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 theLie algebra of geometric vector fields in several cases, including classifyingstacks, quotient stacks of regular Lie groupoids and in particular orbifolds,and foliation groupoids.

On the Lie 2-algebra of sections of an LA-groupoid