Theorems · Definition · category theory
CategoryTheory.cosimplicialSimplicialEquiv
(C : Type u) →
[inst : CategoryTheory.Category.{v, u} C] →
(CategoryTheory.CosimplicialObject C)ᵒᵖ ≌ CategoryTheory.SimplicialObject CᵒᵖThe anti-equivalence between cosimplicial objects and simplicial objects.
- 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.
Cites7
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
- Oppositestatement · cited by 8,081
- SimplexCategorystatement and proof · cited by 2,204
- CategoryTheory.Equivalencestatement · cited by 601
- CategoryTheory.SimplicialObjectstatement · cited by 548
- CategoryTheory.CosimplicialObjectstatement · cited by 125
- CategoryTheory.Functor.opUnopEquivproof · cited by 4
Cited by11
Results whose statement or proof uses this declaration.
- AlgebraicTopology.AlternatingCofaceMapComplex.d_eq_unop_dstatement and proof · cited by 1
- CategoryTheory.cosimplicialSimplicialEquiv_functor_obj_mapstatement and proof · cited by 0
- CategoryTheory.cosimplicialSimplicialEquiv_functor_obj_objstatement and proof · cited by 0
- CategoryTheory.cosimplicialSimplicialEquiv_inverse_mapstatement and proof · cited by 0
- CategoryTheory.cosimplicialSimplicialEquiv_inverse_objstatement and proof · cited by 0
- CategoryTheory.cosimplicialSimplicialEquiv_unitIso_hom_appstatement and proof · cited by 0
- CategoryTheory.cosimplicialSimplicialEquiv_unitIso_inv_appstatement and proof · cited by 0
- AlgebraicTopology.AlternatingCofaceMapComplex.d_squaredproof · cited by 0
- CategoryTheory.cosimplicialSimplicialEquiv_counitIso_hom_app_appstatement and proof · cited by 0
- CategoryTheory.cosimplicialSimplicialEquiv_counitIso_inv_app_appstatement and proof · cited by 0
- CategoryTheory.cosimplicialSimplicialEquiv_functor_map_appstatement and proof · cited by 0