Theorems · Theorem · category theory

HomotopicalAlgebra.BifibrantObject.mk_surjective

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : HomotopicalAlgebra.CategoryWithCofibrations C]
  [inst_2 : CategoryTheory.Limits.HasInitial C] [inst_3 : HomotopicalAlgebra.CategoryWithFibrations C]
  [inst_4 : CategoryTheory.Limits.HasTerminal C] (X : HomotopicalAlgebra.BifibrantObject C),
  ∃ Y,
    ∃ (x : HomotopicalAlgebra.IsCofibrant Y) (x_1 : HomotopicalAlgebra.IsFibrant Y),
      X = HomotopicalAlgebra.BifibrantObject.mk Y

Defined in: Mathlib.AlgebraicTopology.ModelCategory.Bifibrant
Cited by: 0 results in Mathlib
Foundations: Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category HomotopicalAlgebra.CategoryWithCofibrations CategoryTheory.Limits.HasInitial HomotopicalAlgebra.CategoryWithFibrations CategoryTheory.Limits.HasTerminal

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CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.ObjectProperty.FullSubcategory.objproof · cited by 1,316
CategoryTheory.Limits.HasInitialstatement and proof · cited by 185
CategoryTheory.Limits.HasTerminalstatement and proof · cited by 142
CategoryTheory.ObjectProperty.FullSubcategory.propertyproof · cited by 76
HomotopicalAlgebra.IsCofibrantstatement · cited by 56
HomotopicalAlgebra.IsFibrantstatement · cited by 56
HomotopicalAlgebra.CategoryWithFibrationsstatement and proof · cited by 46
HomotopicalAlgebra.CategoryWithCofibrationsstatement and proof · cited by 46
HomotopicalAlgebra.BifibrantObjectstatement and proof · cited by 38
HomotopicalAlgebra.BifibrantObject.mkstatement · cited by 15

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