  We define and study the notion of hyper-K\"ahler category. On the theoretical
side, we focus on construction techniques and deformation theory of such
categories. We also study in details some examples : non-commutative Hilbert
schemes of points on a K3 surface and a categorical resolution of a relative
compactified Prymian constructed by Markushevich and Tikhomirov.

Algebraic Geometry;Category Theory