A 
-structure on a triangulated
category 
is a full subcategory 
with ![F[1] subset= F](/images/equations/t-Structure/Inline4.svg)
such that every object 
fits into a distinguished triangle ![F->E->G->F[1]](/images/equations/t-Structure/Inline6.svg)
, where 
and 
. The orthogonal subcategory is defined by 
for all 
. Its heart ![F intersection F^_|_[1]](/images/equations/t-Structure/Inline11.svg)
is an Abelian
category. The standard example in a derived category
takes 
to be complexes with vanishing positive-degree cohomology
(Bridgeland 2007). Tilting changes this heart by a torsion pair.
t-Structure
See also
Abelian Category, Derived Category, Tilted Heart, Triangulated CategoryExplore with Wolfram|Alpha
References
Bridgeland, T. "Stability Conditions on Triangulated Categories." Ann. Math. 166, 317-345, 2007. https://doi.org/10.4007/annals.2007.166.317.Cite this as:
Weisstein, Eric W. "t-Structure." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/t-Structure.html