Mathlib Map

Theorems · Theorem · category theory

HomotopicalAlgebra.LeftHomotopyClass.sound

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C}
  [inst_1 : HomotopicalAlgebra.CategoryWithWeakEquivalences C] {f g : X ⟶ Y},
  HomotopicalAlgebra.LeftHomotopyRel f g →
    HomotopicalAlgebra.LeftHomotopyClass.mk f = HomotopicalAlgebra.LeftHomotopyClass.mk g
Defined in
Mathlib.AlgebraicTopology.ModelCategory.LeftHomotopy
Cited by
0 results in Mathlib
Foundations
Depth 8 from the axioms · uses Quot.sound
Assumes
CategoryTheory.CategoryHomotopicalAlgebra.CategoryWithWeakEquivalences
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomHomotopicalAlgebra.CategoryWithWeakEquivalences · cited by 77HomotopicalAlgebra.Catego…HomotopicalAlgebra.LeftHomotopyRel · cited by 22HomotopicalAlgebra.LeftHo…HomotopicalAlgebra.LeftHomotopyClass · cited by 15HomotopicalAlgebra.LeftHo…HomotopicalAlgebra.LeftHomotopyClass.mk · cited by 14LeftHomotopyClass.mkLeftHomotopyClass.soundCITED BYCITES

Cites6

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

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.