Theorems · Theorem · category theory

CategoryTheory.Functor.mapProjectiveResolution_complex

∀ {C : Type u} [inst : CategoryTheory.Category.{v_1, u} C] [inst_1 : CategoryTheory.Limits.HasZeroObject C]
  [inst_2 : CategoryTheory.Preadditive C] {D : Type u'} [inst_3 : CategoryTheory.Category.{v', u'} D]
  [inst_4 : CategoryTheory.Limits.HasZeroObject D] [inst_5 : CategoryTheory.Preadditive D]
  [inst_6 : CategoryTheory.CategoryWithHomology D] (F : CategoryTheory.Functor C D) [inst_7 : F.Additive]
  [inst_8 : F.PreservesProjectiveObjects] [inst_9 : F.PreservesHomology] {Z : C}
  (P : CategoryTheory.ProjectiveResolution Z),
  (F.mapProjectiveResolution P).complex = (F.mapHomologicalComplex (ComplexShape.down ℕ)).obj P.complex

Defined in

Mathlib.CategoryTheory.Preadditive.Projective.Resolution

Cited by

0 results in Mathlib

Foundations

Depth 49 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroObjectCategoryTheory.PreadditiveCategoryTheory.CategoryCategoryTheory.Limits.HasZeroObjectCategoryTheory.PreadditiveCategoryTheory.CategoryWithHomologyCategoryTheory.Functor.AdditiveCategoryTheory.Functor.PreservesProjectiveObjectsCategoryTheory.Functor.PreservesHomology