Theorems · Definition · category theory

HomotopicalAlgebra.CofibrantObject.HoCat.adj

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : HomotopicalAlgebra.ModelCategory C] →
      HomotopicalAlgebra.CofibrantObject.HoCat.bifibrantResolution ⊣
        HomotopicalAlgebra.BifibrantObject.HoCat.ιCofibrantObject

The adjunction between the category CofibrantObject.HoCat C and BifibrantObject.HoCat C.

Defined in: Mathlib.AlgebraicTopology.ModelCategory.BifibrantObjectHomotopy
Cited by: 0 results in Mathlib
Foundations: Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category HomotopicalAlgebra.ModelCategory

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CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Iso.homproof · cited by 7,684
CategoryTheory.Adjunctionstatement · cited by 524
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
HomotopicalAlgebra.BifibrantObject.homRelstatement · cited by 22
HomotopicalAlgebra.CofibrantObject.homRelstatement · cited by 20
HomotopicalAlgebra.BifibrantObject.HoCatstatement and proof · cited by 20
HomotopicalAlgebra.CofibrantObject.HoCatstatement and proof · cited by 17

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