Mathlib Map

Theorems · Theorem · category theory

CochainComplex.IsKProjective.leftOrthogonal

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Abelian C]
  (K : CochainComplex C ℤ) [K.IsKProjective],
  (HomotopyCategory.subcategoryAcyclic C).leftOrthogonal ((HomotopyCategory.quotient C (ComplexShape.up ℤ)).obj K)
Defined in
Mathlib.Algebra.Homology.HomotopyCategory.KProjective
Cited by
1 results in Mathlib
Foundations
Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.AbelianCochainComplex.IsKProjective
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CochainComplex.IsKProjective.Qh_map_bijective · cited by 2IsKProjective.Qh_map_bije…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Abelian · cited by 1753CategoryTheory.AbelianHomologicalComplex · cited by 1691HomologicalComplexComplexShape.up · cited by 1123ComplexShape.upCochainComplex · cited by 1016CochainComplexHomotopyCategory · cited by 132HomotopyCategoryHomotopyCategory.quotient · cited by 109HomotopyCategory.quotientCochainComplex.IsKProjective · cited by 15CochainComplex.IsKProject…HomotopyCategory.subcategoryAcyclic · cited by 10HomotopyCategory.subcateg…CategoryTheory.ObjectProperty.leftOrthogonal · cited by 5ObjectProperty.leftOrthog…CochainComplex.isKProjective_iff_leftOrthogonal · cited by 1CochainComplex.isKProject…IsKProjective.leftOrthogonalCITED BYCITES

Cites12

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.