t-structure

Summary

A t-structure on a triangulated category is a pair of full subcategories, of "non-positive" and "non-negative" objects. They behave like the complexes with cohomology only in degrees $\le 0$ and $\ge 0$ in a derived category. It gives truncation functors and cohomology functors with values in its heart, which is always an abelian category. t-structures were introduced by Beilinson, Bernstein and Deligne to construct perverse sheaves as the heart of a non-standard t-structure.