##  [T-Structure](/t-structure) 

  ##  [T-Structure](https://algebra.quantumdictionary.io/t-structure-0) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A pair (D^{≤0}, D^{≥0}) of full subcategories of a triangulated category D, closed under shifts and extensions, whose intersection (the heart) is an abelian category; t-structures organize cohomological truncations and produce cohomology functors H^i.