Theorems · Theorem · category theory

HomotopicalAlgebra.fibration_op_iff

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} (f : X ⟶ Y)
  [inst_1 : HomotopicalAlgebra.CategoryWithCofibrations C],
  HomotopicalAlgebra.Fibration f.op ↔ HomotopicalAlgebra.Cofibration f

Defined in: Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations
Cited by: 0 results in Mathlib
Foundations: Depth 12 from the axioms · uses propext
Assumes: CategoryTheory.Category HomotopicalAlgebra.CategoryWithCofibrations

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CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
Oppositestatement and proof · cited by 8,081
Quiver.Hom.opstatement and proof · cited by 1,948
HomotopicalAlgebra.CategoryWithCofibrationsstatement and proof · cited by 46
HomotopicalAlgebra.fibrationsproof · cited by 40
HomotopicalAlgebra.Fibrationstatement · cited by 32
HomotopicalAlgebra.Cofibrationstatement · cited by 27

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