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In this thesis, we introduce a new cohomology theory associated to a Lie2-algebras and a new cohomology theory associated to a Lie 2-group. Thesecohomology theories are shown to extend the classical cohomology theories ofLie algebras and Lie groups in that their second groups classify extensions. Weuse this fact together with an adapted van Est map to prove the integrabilityof Lie 2-algebras anew.

A cohomology theory for Lie 2-algebras and Lie 2-groups