Theorems · Theorem · category theory

AlgebraicTopology.AlternatingCofaceMapComplex.d_eq_unop_d

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
  (X : CategoryTheory.CosimplicialObject C) (n : ℕ),
  AlgebraicTopology.AlternatingCofaceMapComplex.objD X n =
    (AlgebraicTopology.AlternatingFaceMapComplex.objD
        ((CategoryTheory.cosimplicialSimplicialEquiv C).functor.obj (Opposite.op X)) n).unop

Defined in: Mathlib.AlgebraicTopology.AlternatingFaceMapComplex
Cited by: 1 results in Mathlib
Foundations: Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Preadditive

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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 and proof · cited by 19,642
Oppositestatement · cited by 8,081
Finset.sumproof · cited by 5,195
Finset.univproof · cited by 3,473
CategoryTheory.Preadditivestatement and proof · cited by 3,309
SimplexCategorystatement · cited by 2,204
CategoryTheory.Equivalence.functorstatement and proof · cited by 1,268
Quiver.Hom.unopstatement · cited by 903
CategoryTheory.SimplicialObjectstatement · cited by 548
CategoryTheory.SimplicialObject.δproof · cited by 188

Cited by1

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AlgebraicTopology.AlternatingCofaceMapComplex.d_squaredproof · cited by 0