Categorified central extensions, \'etale Lie 2-groups and Lie's Third Theorem for locally exponential Lie algebras

Understand

Lie's Third Theorem, asserting that each finite-dimensional Lie algebra is the Lie algebra of a Lie group, fails in infinite dimensions.

• The modern account on this phenomenon is the integration problem for central extensions of infinite-dimensional Lie algebras, which in turn is phrased in terms of an integration procedure for Lie algebra cocycles.
• This paper remedies the obstructions for integrating cocycles and central extensions from Lie algebras to Lie groups by generalising the integrating objects.
• Those objects obey the maximal coherence that one can expect.