Theorems · Theorem · category theory
CategoryTheory.Quotient.sound
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] (r : HomRel C) {a b : C} {f₁ f₂ : a ⟶ b},
r f₁ f₂ → (CategoryTheory.Quotient.functor r).map f₁ = (CategoryTheory.Quotient.functor r).map f₂- Defined in
- Mathlib.CategoryTheory.Quotient
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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.Functor.objstatement · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Functor.mapstatement · cited by 8,698
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- CategoryTheory.Category.comp_idproof · cited by 2,119
- CategoryTheory.Category.id_compproof · cited by 1,998
- HomRelstatement and proof · cited by 49
- CategoryTheory.Quotientstatement · cited by 48
- CategoryTheory.Quotient.functorstatement · cited by 41
- CategoryTheory.HomRel.CompClosureproof · cited by 19
Cited by16
Results whose statement or proof uses this declaration.
- HomotopyCategory.eq_of_homotopyproof · cited by 7
- SSet.Truncated.HomotopyCategory.homMk_comp_homMkproof · cited by 3
- CategoryTheory.Preadditive.RightFreyd.eq_of_rightHomotopyproof · cited by 3
- SimplexCategoryGenRel.σ_comp_σproof · cited by 2
- CategoryTheory.Cat.FreeRefl.homMk_idproof · cited by 2
- SimplexCategoryGenRel.δ_comp_δproof · cited by 2
- CategoryTheory.Quotient.lift_unique'proof · cited by 2
- SimplexCategoryGenRel.δ_comp_σ_succproof · cited by 1
- HomotopicalAlgebra.FibrantObject.toHoCat_map_eqproof · cited by 1
- HomotopicalAlgebra.CofibrantObject.toHoCat_map_eqproof · cited by 1
- SimplexCategoryGenRel.δ_comp_σ_selfproof · cited by 1
- SimplexCategoryGenRel.δ_comp_σ_of_gtproof · cited by 1