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In this paper, we introduce the notion of a pre-Lie 2-algebra, which is acategorification of a pre-Lie algebra. We prove that the category of pre-Lie2-algebras and the category of 2-term pre-Lie$_\infty$-algebras are equivalent.We classify skeletal pre-Lie 2-algebras by the third cohomology of a pre-Liealgebra. We prove that crossed modules of pre-Lie algebras are in one-to-onecorrespondence with strict pre-Lie 2-algebras. $\mathcal O$-operators on Lie2-algebras are introduced, which can be used to construct pre-Lie 2-algebras.As an application, we give solutions of 2-graded classical Yang-Baxterequations in some semidirect product Lie 2-algebras.

Categorification of Pre-Lie Algebras and Solutions of 2-graded Classical Yang-Baxter Equations