Theorems · Theorem · category theory

CategoryTheory.Pretriangulated.contractibleTriangleFunctor_obj

∀ (C : Type u) [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.HasShift C ℤ]
  [inst_2 : CategoryTheory.Limits.HasZeroObject C] [inst_3 : CategoryTheory.Limits.HasZeroMorphisms C] (X : C),
  (CategoryTheory.Pretriangulated.contractibleTriangleFunctor C).obj X =
    CategoryTheory.Pretriangulated.contractibleTriangle X

Defined in: Mathlib.CategoryTheory.Triangulated.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.HasShift CategoryTheory.Limits.HasZeroObject CategoryTheory.Limits.HasZeroMorphisms

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CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Functor.objstatement and proof · cited by 19,642
CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
CategoryTheory.HasShiftstatement and proof · cited by 1,527
CategoryTheory.Limits.HasZeroObjectstatement and proof · cited by 1,298
CategoryTheory.Pretriangulated.Trianglestatement · cited by 645
CategoryTheory.Pretriangulated.contractibleTrianglestatement · cited by 27
CategoryTheory.Pretriangulated.contractibleTriangleFunctorstatement and proof · cited by 5

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