Mathlib Map

Theorems · Definition · category theory

HomotopicalAlgebra.CofibrantObject.bifibrantResolutionObj

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

Given X : CofibrantObject C, this is a choice of bifibrant resolution of X.

Defined in
Mathlib.AlgebraicTopology.ModelCategory.BifibrantObjectHomotopy
Cited by
13 results in Mathlib
Foundations
Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryHomotopicalAlgebra.ModelCategory
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

HomotopicalAlgebra.CofibrantObject.iBifibrantResolutionObj · cited by 9CofibrantObject.iBifibran…HomotopicalAlgebra.CofibrantObject.bifibrantResolutionMap · cited by 6CofibrantObject.bifibrant…HomotopicalAlgebra.CofibrantObject.HoCat.bifibrantResolution' · cited by 2HoCat.bifibrantResolution'HomotopicalAlgebra.CofibrantObject.bifibrantResolutionMap_fac · cited by 2CofibrantObject.bifibrant…HomotopicalAlgebra.CofibrantObject.bifibrantResolutionMap_fac' · cited by 1CofibrantObject.bifibrant…HomotopicalAlgebra.CofibrantObject.exists_bifibrant_map · cited by 1CofibrantObject.exists_bi…HomotopicalAlgebra.CofibrantObject.HoCat.adjCounit'_app · cited by 0HoCat.adjCounit'_appHomotopicalAlgebra.CofibrantObject.HoCat.adjCounitIso_inv_app · cited by 0HoCat.adjCounitIso_inv_appHomotopicalAlgebra.CofibrantObject.HoCat.adjUnit_app · cited by 0HoCat.adjUnit_appHomotopicalAlgebra.CofibrantObject.HoCat.bifibrantResolution'_map · cited by 0HoCat.bifibrantResolution…HomotopicalAlgebra.CofibrantObject.HoCat.bifibrantResolution'_obj · cited by 0HoCat.bifibrantResolution…HomotopicalAlgebra.CofibrantObject.bifibrantResolutionMap_fac'_assoc · cited by 0CofibrantObject.bifibrant…HomotopicalAlgebra.CofibrantObject.bifibrantResolutionMap_fac_assoc · cited by 0CofibrantObject.bifibrant…HomotopicalAlgebra.CofibrantObject.HoCat.bifibrantResolution_map · cited by 0HoCat.bifibrantResolution…HomotopicalAlgebra.CofibrantObject.bifibrantResolutionObj_hom_ext · cited by 0CofibrantObject.bifibrant…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryHomotopicalAlgebra.ModelCategory · cited by 141HomotopicalAlgebra.ModelC…HomotopicalAlgebra.BifibrantObject · cited by 38HomotopicalAlgebra.Bifibr…HomotopicalAlgebra.CofibrantObject · cited by 35HomotopicalAlgebra.Cofibr…HomotopicalAlgebra.CofibrantObject.exists_bifibrant · cited by 0CofibrantObject.exists_bi…CofibrantObject.bifibrantReso…CITED BYCITES

Cites5

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

Cited by16

Results whose statement or proof uses this declaration.