Theorems · Theorem · category theory

CategoryTheory.ObjectProperty.inverseImage_trW_iff

∀ {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]
  {D : Type u_2} [inst_6 : CategoryTheory.Category.{v_2, u_2} D] [inst_7 : CategoryTheory.Preadditive D]
  [inst_8 : CategoryTheory.Limits.HasZeroObject D] [inst_9 : CategoryTheory.HasShift D ℤ]
  [inst_10 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor D n).Additive] [inst_11 : CategoryTheory.Pretriangulated D]
  (P : CategoryTheory.ObjectProperty C) (F : CategoryTheory.Functor D C) [inst_12 : F.CommShift ℤ] [F.IsTriangulated]
  [P.IsClosedUnderIsomorphisms] {X Y : D} (s : X ⟶ Y), (P.inverseImage F).trW s ↔ P.trW (F.map s)

Defined in

Mathlib.CategoryTheory.Triangulated.Subcategory

Cited by

0 results in Mathlib

Foundations

Depth 52 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroObjectCategoryTheory.HasShiftCategoryTheory.PreadditiveCategoryTheory.Functor.AdditiveCategoryTheory.PretriangulatedCategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasZeroObjectCategoryTheory.HasShiftCategoryTheory.Functor.AdditiveCategoryTheory.PretriangulatedCategoryTheory.Functor.CommShiftCategoryTheory.Functor.IsTriangulatedCategoryTheory.ObjectProperty.IsClosedUnderIsomorphisms