Theorems · Theorem · category theory
CategoryTheory.Subobject.factorThru_eq_zero
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
{X Y : C} {P : CategoryTheory.Subobject Y} {f : X ⟶ Y} {h : P.Factors f}, P.factorThru f h = 0 ↔ f = 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.Subobjectstatement and proof · cited by 385
- CategoryTheory.Limits.zero_compproof · cited by 339
- CategoryTheory.Subobject.underlyingstatement · cited by 211
- CategoryTheory.Subobject.arrowproof · cited by 175
- CategoryTheory.eq_whiskerproof · cited by 66
- CategoryTheory.Subobject.Factorsstatement and proof · cited by 56
- CategoryTheory.Subobject.factorThrustatement and proof · cited by 35
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicTopology.NormalizedMooreComplex.d_squaredproof · cited by 0