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Theorems · Definition · category theory

CategoryTheory.cosimplicialSimplicialEquiv

(C : Type u) →
  [inst : CategoryTheory.Category.{v, u} C] →
    (CategoryTheory.CosimplicialObject C)ᵒᵖ ≌ CategoryTheory.SimplicialObject Cᵒᵖ

The anti-equivalence between cosimplicial objects and simplicial objects.

Defined in
Mathlib.AlgebraicTopology.SimplicialObject.Basic
Cited by
11 results in Mathlib
Foundations
Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.Category

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AlgebraicTopology.AlternatingCofaceMapComplex.d_eq_unop_d · cited by 1AlternatingCofaceMapCompl…CategoryTheory.cosimplicialSimplicialEquiv_functor_obj_map · cited by 0CategoryTheory.cosimplici…CategoryTheory.cosimplicialSimplicialEquiv_functor_obj_obj · cited by 0CategoryTheory.cosimplici…CategoryTheory.cosimplicialSimplicialEquiv_inverse_map · cited by 0CategoryTheory.cosimplici…CategoryTheory.cosimplicialSimplicialEquiv_inverse_obj · cited by 0CategoryTheory.cosimplici…CategoryTheory.cosimplicialSimplicialEquiv_unitIso_hom_app · cited by 0CategoryTheory.cosimplici…CategoryTheory.cosimplicialSimplicialEquiv_unitIso_inv_app · cited by 0CategoryTheory.cosimplici…AlgebraicTopology.AlternatingCofaceMapComplex.d_squared · cited by 0AlternatingCofaceMapCompl…CategoryTheory.cosimplicialSimplicialEquiv_counitIso_hom_app_app · cited by 0CategoryTheory.cosimplici…CategoryTheory.cosimplicialSimplicialEquiv_counitIso_inv_app_app · cited by 0CategoryTheory.cosimplici…CategoryTheory.cosimplicialSimplicialEquiv_functor_map_app · cited by 0CategoryTheory.cosimplici…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryOpposite · cited by 8081OppositeSimplexCategory · cited by 2204SimplexCategoryCategoryTheory.Equivalence · cited by 601CategoryTheory.EquivalenceCategoryTheory.SimplicialObject · cited by 548CategoryTheory.Simplicial…CategoryTheory.CosimplicialObject · cited by 125CategoryTheory.Cosimplici…CategoryTheory.Functor.opUnopEquiv · cited by 4Functor.opUnopEquivCategoryTheory.cosimplicialSi…CITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by11

Results whose statement or proof uses this declaration.