Theorems · Theorem · category theory

CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_inv_app

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.HasShift C ℤ] (X : C) (n m : ℤ)
  (hnm : autoParam (n + m = 0) CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_inv_app._auto_1),
  (CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso C n).inv.app X =
    CategoryTheory.CategoryStruct.comp
      ((CategoryTheory.Pretriangulated.shiftFunctorOpIso Cᵒᵖ n m hnm).hom.app (Opposite.op (Opposite.op X)))
      ((CategoryTheory.Pretriangulated.shiftFunctorOpIso C m n ⋯).inv.app (Opposite.op X)).op

Defined in: Mathlib.CategoryTheory.Triangulated.Opposite.OpOp
Cited by: 2 results in Mathlib
Foundations: Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.HasShift

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Cites17

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
Quiver.Homstatement · cited by 32,603
CategoryTheory.Functor.objstatement · cited by 19,642
CategoryTheory.CategoryStruct.compstatement · cited by 17,999
CategoryTheory.Functorstatement · cited by 16,252
Oppositestatement · cited by 8,081
CategoryTheory.Iso.homstatement · cited by 7,684
CategoryTheory.NatTrans.appstatement and proof · cited by 7,406
CategoryTheory.Functor.compstatement · cited by 6,529
CategoryTheory.Iso.invstatement and proof · cited by 6,514
Quiver.Hom.opstatement · cited by 1,948
CategoryTheory.shiftFunctorstatement · cited by 1,553

Cited by2

Results whose statement or proof uses this declaration.

CategoryTheory.Pretriangulated.commShiftIso_opOp_inv_appproof · cited by 1
CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_inv_app_assocproof · cited by 0