Theorems · Definition · category theory

HomotopicalAlgebra.CofibrantObject.HoCat.adjCounitIso

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : HomotopicalAlgebra.ModelCategory C] →
      HomotopicalAlgebra.BifibrantObject.HoCat.ιCofibrantObject.comp
          HomotopicalAlgebra.CofibrantObject.HoCat.bifibrantResolution ≅
        CategoryTheory.Functor.id (HomotopicalAlgebra.BifibrantObject.HoCat C)

Auxiliary definition for CofibrantObject.HoCat.adj.

Defined in: Mathlib.AlgebraicTopology.ModelCategory.BifibrantObjectHomotopy
Cited by: 1 results in Mathlib
Foundations: Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category HomotopicalAlgebra.ModelCategory

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

Cites19

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
CategoryTheory.Functorstatement · cited by 16,252
CategoryTheory.Functor.compstatement · cited by 6,529
CategoryTheory.Isostatement · cited by 3,963
CategoryTheory.Functor.idstatement · cited by 3,333
CategoryTheory.Iso.symmproof · cited by 993
CategoryTheory.asIsoproof · cited by 177
HomotopicalAlgebra.ModelCategorystatement and proof · cited by 141
HomotopicalAlgebra.BifibrantObjectstatement · cited by 38
HomotopicalAlgebra.bifibrantObjectsstatement · cited by 37
HomotopicalAlgebra.CofibrantObjectstatement · cited by 35
HomotopicalAlgebra.cofibrantObjectsstatement · cited by 34

Cited by2

Results whose statement or proof uses this declaration.

HomotopicalAlgebra.CofibrantObject.HoCat.adjproof · cited by 0
HomotopicalAlgebra.CofibrantObject.HoCat.adjCounitIso_inv_appstatement · cited by 0