Theorems · Definition · category theory
HomotopicalAlgebra.LeftHomotopyClass.mk
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
{X Y : C} →
[inst_1 : HomotopicalAlgebra.CategoryWithWeakEquivalences C] → (X ⟶ Y) → HomotopicalAlgebra.LeftHomotopyClass X YGiven f : X ⟶ Y, this is the class of f in the quotient LeftHomotopyClass X Y.
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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 · cited by 32,603
- HomotopicalAlgebra.CategoryWithWeakEquivalencesstatement and proof · cited by 77
- HomotopicalAlgebra.LeftHomotopyRelproof · cited by 22
- HomotopicalAlgebra.LeftHomotopyClassstatement · cited by 15
Cited by16
Results whose statement or proof uses this declaration.
- HomotopicalAlgebra.leftHomotopyClassEquivRightHomotopyClassproof · cited by 4
- HomotopicalAlgebra.LeftHomotopyClass.mk_surjectivestatement · cited by 4
- HomotopicalAlgebra.LeftHomotopyClass.postcompproof · cited by 4
- HomotopicalAlgebra.LeftHomotopyClass.mk_eq_mk_iffstatement and proof · cited by 3
- HomotopicalAlgebra.bijective_rightHomotopyClassToHomproof · cited by 2
- HomotopicalAlgebra.leftHomotopyClassEquivRightHomotopyClass_mkstatement · cited by 0
- HomotopicalAlgebra.leftHomotopyClassEquivRightHomotopyClass_symm_mkstatement · cited by 0
- HomotopicalAlgebra.leftHomotopyClassToHom_mkstatement · cited by 0
- HomotopicalAlgebra.LeftHomotopyClass.postcomp_mkstatement · cited by 0