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  "body": "\n## Summary\n\nA t-structure on a [[triangulated category|T2V7GJJ2EN]] is a pair of full subcategories, of \"non-positive\" and \"non-negative\" objects.\nThey behave like the complexes with cohomology only in degrees $\\le 0$ and $\\ge 0$ in a [[derived category|5ST7NVJFSM]].\nIt gives truncation functors and cohomology functors with values in its heart, which is always an abelian category.\nt-structures were introduced by Beilinson, Bernstein and Deligne to construct perverse sheaves as the heart of a non-standard t-structure.\n\n## Explanations\n\n### L1 human\n\nIn the derived category of an abelian category, a complex can be cut into its low degree part and its high degree part.\nThe original abelian category is recovered as the complexes with cohomology only in degree $0$.\nA t-structure is an abstract way of making such a cut in any triangulated category.\nDifferent t-structures on the same triangulated category can have quite different hearts.\nThis is how one category can hide several abelian categories, such as sheaves and perverse sheaves.\n",
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