Theorems · Theorem · category theory
CategoryTheory.Triangulated.TStructure.Heart.essImage_eq_heart
∀ {C : Type u} {inst : CategoryTheory.Category.{v, u} C} {inst_1 : CategoryTheory.Preadditive C}
{inst_2 : CategoryTheory.Limits.HasZeroObject C} {inst_3 : CategoryTheory.HasShift C ℤ}
{inst_4 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive} {inst_5 : CategoryTheory.Pretriangulated C}
{t : CategoryTheory.Triangulated.TStructure C} {H : Type u'} {inst_6 : CategoryTheory.Category.{v', u'} H}
{inst_7 : CategoryTheory.Preadditive H} [self : t.Heart H],
(CategoryTheory.Triangulated.TStructure.Heart.ι t).essImage = t.heart- Cited by
- 1 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- CategoryTheory.shiftFunctorstatement and proof · cited by 1,553
- CategoryTheory.HasShiftstatement and proof · cited by 1,527
- CategoryTheory.Limits.HasZeroObjectstatement and proof · cited by 1,298
- CategoryTheory.Functor.Additivestatement and proof · cited by 1,179
- CategoryTheory.ObjectPropertystatement · cited by 798
- CategoryTheory.Pretriangulatedstatement and proof · cited by 669
- CategoryTheory.Triangulated.TStructurestatement and proof · cited by 318
- CategoryTheory.Functor.essImagestatement · cited by 82
- CategoryTheory.Triangulated.TStructure.Heartstatement and proof · cited by 6
- CategoryTheory.Triangulated.TStructure.heartstatement · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.Triangulated.TStructure.essImage_ιHeartproof · cited by 1