Theorems · Theorem · algebraic topology

AlgebraicTopology.DoldKan.Q_f_naturality

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C] (q n : ℕ)
  {X Y : CategoryTheory.SimplicialObject C} (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp (f.app (Opposite.op { len := n })) ((AlgebraicTopology.DoldKan.Q q).f n) =
    CategoryTheory.CategoryStruct.comp ((AlgebraicTopology.DoldKan.Q q).f n) (f.app (Opposite.op { len := n }))

Defined in: Mathlib.AlgebraicTopology.DoldKan.Projections
Cited by: 2 results in Mathlib
Foundations: Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Preadditive

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Cites21

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 and proof · cited by 32,603
CategoryTheory.Functor.objstatement · cited by 19,642
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
Oppositestatement · cited by 8,081
CategoryTheory.NatTrans.appstatement and proof · cited by 7,406
CategoryTheory.CategoryStruct.idproof · cited by 6,235
CategoryTheory.Preadditivestatement and proof · cited by 3,309
SimplexCategorystatement · cited by 2,204
CategoryTheory.Category.comp_idproof · cited by 2,119
CategoryTheory.Category.id_compproof · cited by 1,998
HomologicalComplex.Xstatement and proof · cited by 1,839

Cited by2

Results whose statement or proof uses this declaration.

AlgebraicTopology.DoldKan.QInfty_f_naturalityproof · cited by 1
AlgebraicTopology.DoldKan.Q_f_naturality_assocproof · cited by 0