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Theorems · Definition · category theory

HomotopicalAlgebra.cofibrations

(C : Type u) →
  [inst : CategoryTheory.Category.{v, u} C] →
    [HomotopicalAlgebra.CategoryWithCofibrations C] → CategoryTheory.MorphismProperty C

The class of cofibrations in a category with cofibrations.

Defined in
Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations
Cited by
37 results in Mathlib
Foundations
Depth 4 from the axioms · uses no axioms
Assumes
CategoryTheory.CategoryHomotopicalAlgebra.CategoryWithCofibrations

Around this declaration

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

HomotopicalAlgebra.trivialCofibrations · cited by 31HomotopicalAlgebra.trivia…HomotopicalAlgebra.CofibrantBrownFactorization.toMapFactorizationData · cited by 6CofibrantBrownFactorizati…HomotopicalAlgebra.Cylinder.ofFactorizationData · cited by 6Cylinder.ofFactorizationD…HomotopicalAlgebra.CofibrantBrownFactorization.mk' · cited by 4CofibrantBrownFactorizati…HomotopicalAlgebra.CofibrantBrownFactorization.s · cited by 4CofibrantBrownFactorizati…HomotopicalAlgebra.cofibration_iff · cited by 4HomotopicalAlgebra.cofibr…HomotopicalAlgebra.RightHomotopyRel.exists_very_good_pathObject · cited by 3RightHomotopyRel.exists_v…HomotopicalAlgebra.isCofibrant_of_cofibration · cited by 3HomotopicalAlgebra.isCofi…HomotopicalAlgebra.mem_cofibrations · cited by 2HomotopicalAlgebra.mem_co…HomotopicalAlgebra.Cylinder.exists_very_good · cited by 2Cylinder.exists_very_goodHomotopicalAlgebra.CofibrantBrownFactorization.mk.inj · cited by 1mk.injHomotopicalAlgebra.CofibrantBrownFactorization.mk.noConfusion · cited by 1mk.noConfusionHomotopicalAlgebra.CofibrantBrownFactorization.s_p · cited by 1CofibrantBrownFactorizati…HomotopicalAlgebra.CofibrantBrownFactorization.s_p_assoc · cited by 1CofibrantBrownFactorizati…HomotopicalAlgebra.CofibrantObject.HoCat.exists_resolution · cited by 1HoCat.exists_resolutionCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.MorphismProperty · cited by 2179CategoryTheory.MorphismPr…HomotopicalAlgebra.CategoryWithCofibrations · cited by 46HomotopicalAlgebra.Catego…HomotopicalAlgebra.CategoryWithCofibrations.cofibrations · cited by 0CategoryWithCofibrations.…HomotopicalAlgebra.cofibratio…CITED BYCITES

Cites4

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

Cited by56

Results whose statement or proof uses this declaration.