Theorems · Definition · category theory

HomotopicalAlgebra.LeftHomotopyClass.postcomp

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X Y Z : C} →
      [inst_1 : HomotopicalAlgebra.CategoryWithWeakEquivalences C] →
        HomotopicalAlgebra.LeftHomotopyClass X Y → (Y ⟶ Z) → HomotopicalAlgebra.LeftHomotopyClass X Z

The postcomposition map LeftHomotopyClass X Y → (Y ⟶ Z) → LeftHomotopyClass X Z.

Defined in: Mathlib.AlgebraicTopology.ModelCategory.LeftHomotopy
Cited by: 4 results in Mathlib
Foundations: Depth 14 from the axioms · uses propext, Quot.sound
Assumes: CategoryTheory.Category HomotopicalAlgebra.CategoryWithWeakEquivalences

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Cites6

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

CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compproof · cited by 17,999
HomotopicalAlgebra.CategoryWithWeakEquivalencesstatement and proof · cited by 77
HomotopicalAlgebra.LeftHomotopyClassstatement and proof · cited by 15
HomotopicalAlgebra.LeftHomotopyClass.mkproof · cited by 14

Cited by4

Results whose statement or proof uses this declaration.

HomotopicalAlgebra.LeftHomotopyClass.postcomp_bijective_of_fibration_of_weakEquivalencestatement and proof · cited by 3
HomotopicalAlgebra.bijective_rightHomotopyClassToHomproof · cited by 2
HomotopicalAlgebra.LeftHomotopyClass.postcomp_bijective_of_weakEquivalencestatement and proof · cited by 0
HomotopicalAlgebra.LeftHomotopyClass.postcomp_mkstatement · cited by 0