t-structures Triangulated category

verdier introduced triangulated categories in order place derived categories in category-theoretic context: every abelian category there exists triangulated category



d
(
a
)


{\displaystyle d(a)}

, containing full subcategory (the 0-complexes concentrated in cohomological degree 0), , in can construct derived functors. different abelian categories can give rise equivalent derived categories, impossible reconstruct triangulated category



d
(
a
)


{\displaystyle d(a)}

.

a partial solution problem, impose t-structure on triangulated category d. different t-structures on d give rise different abelian categories inside it. notion presented in (beilinson, bernstein & deligne 1982).