Theorems · Theorem · category theory

CategoryTheory.ObjectProperty.extensionProductIter_bot

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroObject C]
  [inst_2 : CategoryTheory.HasShift C ℤ] [inst_3 : CategoryTheory.Preadditive C]
  [inst_4 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive] [inst_5 : CategoryTheory.Pretriangulated C] (n : ℕ),
  ⊥.extensionProductIter n = ⊥

Defined in: Mathlib.CategoryTheory.Triangulated.Subcategory
Cited by: 1 results in Mathlib
Foundations: Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroObject CategoryTheory.HasShift CategoryTheory.Preadditive CategoryTheory.Functor.Additive CategoryTheory.Pretriangulated

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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
Bot.botstatement and proof · cited by 4,720
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 and proof · cited by 798
CategoryTheory.Pretriangulatedstatement and proof · cited by 669
CategoryTheory.ObjectProperty.extensionProductIterstatement and proof · cited by 20
CategoryTheory.ObjectProperty.extensionProductIter_succproof · cited by 8
CategoryTheory.ObjectProperty.extensionProductIter_zeroproof · cited by 5

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.ObjectProperty.monotone'_triangEnvelopeIterproof · cited by 1