I will first give an introduction to Nichols algebras, also in the non-diagonal setting. I will then explain my folding construction, which turns a Nichols algebra with a diagram automorphism into a new Nichols algebra, and by which I was able to construct new families of Nichols algebras over nonabelian groups. I also put this construction into a broader systematic context of category extension, and I explain recent joint work with Angiono and Sanmarco building on work by Heckenberger and Vendramin, in which we show that all Nichols algebras over nonabelian groups with rank larger than 3 arise in this way.

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