Theorems · Inductive type · category theory
HomotopicalAlgebra.CategoryWithWeakEquivalences
(C : Type u) → [CategoryTheory.Category.{v, u} C] → Type (max u v)A category with weak equivalences is a category equipped with a class of morphisms named "weak equivalences".
- Cited by
- 77 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
Cited by143
Results whose statement or proof uses this declaration.
- HomotopicalAlgebra.WeakEquivalencestatement · cited by 45
- HomotopicalAlgebra.weakEquivalencesstatement and proof · cited by 44
- HomotopicalAlgebra.PathObjectstatement · cited by 32
- HomotopicalAlgebra.Cylinderstatement · cited by 31
- HomotopicalAlgebra.trivialCofibrationsstatement and proof · cited by 31
- HomotopicalAlgebra.trivialFibrationsstatement and proof · cited by 30
- HomotopicalAlgebra.PathObject.toPrepathObjectstatement and proof · cited by 24
- HomotopicalAlgebra.Cylinder.toPrecylinderstatement and proof · cited by 23
- HomotopicalAlgebra.LeftHomotopyRelstatement and proof · cited by 22
- HomotopicalAlgebra.RightHomotopyRelstatement and proof · cited by 22
- HomotopicalAlgebra.RightHomotopyClass.mkstatement and proof · cited by 17
- HomotopicalAlgebra.RightHomotopyClassstatement and proof · cited by 16