nLab exceptional collection

Idea

In a derived category of chain complexes, or more generally in a triangulated category or in fact in a stable (infinity,1)-category, an exceptional collection of object is a set of objects such that the Ext-groups (hom-spaces) between them are concentrated in degree 0. It is a full exceptional collection if in addition it generates the category.

References

In

• Alexei Bondal, Helices, representations of quivers and Koszul algebras, in Helices and vector bundles, vol. 148 of London Math. Soc. Lecture Note Ser., pp. 75–95. Cambridge Univ. Press, Cambridge, 1990.

an exceptional collection in the derived category of coherent sheaveson a suitable Calabi-Yau variety cone is used to induce a quiver and make the derived category be equivalent to that of its quiver representations.

See also

• Agnieszka Bodzenta, DG categories and exceptional collections (arXiv:1205.6148)