The paper under review treats deformation theory in noncommutative algebraic geometry. For a Grothendieck category \(\mathcal{C}\) which, via a \(\mathbb{Z}\)-generating sequence \((\mathcal{O}(n))_{n \in \mathbb{Z}}\), is equivalent to the category of “quasi-coherent modules” over an associated \(\mathbb{Z}\)-algebra \(\mathfrak{a}\), the authors show that under suitable cohomological conditions “taking quasi-coherent modules” defines an equivalence between linear deformations of \(\mathfrak{a}\) and abelian deformations of \(\mathcal{C}\). If \((\mathcal{O}(n))_{n \in \mathbb{Z}}\) at the same time a geometric helix in the derived category, it is shown that restricting a (deformed) \(\mathbb{Z}\)-algebra to a “thread” of objects defines a further equivalence with linear deformations of the associated matrix algebra.