Title: Higher internal covers
Abstract: Internal covers describe a situation where two definable sets admit a definable bijection over some additional parameters. In this case, the automorphism group of one of them over the other becomes definable, yielding a definable version of Galois theory. Hrushovski realized that it is more canonical to attach a groupoid, rather than a group to such covers, and there is an equivalence between such covers and definable groupoids in the base theory. I will suggest a notion of ``higher'' internal covers, corresponding to higher definable groupoids.