Theorems · Theorem · category theory
CategoryTheory.Limits.equalizerSubobject_factors
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} (f g : X ⟶ Y)
[inst_1 : CategoryTheory.Limits.HasEqualizer f g] {W : C} (h : W ⟶ X),
CategoryTheory.CategoryStruct.comp h f = CategoryTheory.CategoryStruct.comp h g →
(CategoryTheory.Limits.equalizerSubobject f g).Factors h- Defined in
- Mathlib.CategoryTheory.Subobject.Limits
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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.compstatement and proof · cited by 17,999
- CategoryTheory.Limits.limit.lift_πproof · cited by 266
- CategoryTheory.Limits.Fork.ofιproof · cited by 66
- CategoryTheory.Subobject.Factorsstatement · cited by 56
- CategoryTheory.Limits.HasEqualizerstatement and proof · cited by 47
- CategoryTheory.Limits.equalizer.liftproof · cited by 19
- CategoryTheory.Limits.equalizerSubobjectstatement · cited by 10
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.equalizerSubobject_factors_iffproof · cited by 0
- CategoryTheory.Limits.pullback_equalizerproof · cited by 0