What is "t-structure"

In mathematics, more specifically in homological algebra, a t-structure is an additional piece of structure that can be put on a triangulated category or a stable infinity category that axiomatizes the properties of complexes whose positive or negative cohomology vanishes. The notion was introduced by Beilinson, Bernstein and Deligne. It allows to construct an abelian category, namely the heart of the t-structure, from a triangulated category.