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Calabi-Yau manifolds are higher dimensional generalizations of elliptic curves and K3 surfaces. They can be defined as the compact complex Kähler manifolds with trivial canonical bundle, and play a central role in mirror symmetry. This tag can also be used for Calabi-Yau algebras and categories. These algebraic notions are inspired by the properties of the derived categories of coherent sheaves on Calabi-Yau manifolds.
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Which cluster algebras have been categorified?
There are several different questions in here and what follows are only partial answers to some of these, mostly consisting of pointers to pieces of the literature.
"In what other instances have clu …