Theorems · Theorem · category theory
CategoryTheory.Limits.PullbackCone.IsLimit.hom_ext
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y Z : C} {f : X ⟶ Z} {g : Y ⟶ Z}
{t : CategoryTheory.Limits.PullbackCone f g} (ht : CategoryTheory.Limits.IsLimit t) {W : C} {k l : W ⟶ t.pt},
CategoryTheory.CategoryStruct.comp k t.fst = CategoryTheory.CategoryStruct.comp l t.fst →
CategoryTheory.CategoryStruct.comp k t.snd = CategoryTheory.CategoryStruct.comp l t.snd → k = l- Cited by
- 11 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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.WalkingPairstatement · cited by 1,319
- CategoryTheory.Limits.Cone.ptstatement and proof · cited by 1,298
- CategoryTheory.Limits.IsLimitstatement and proof · cited by 664
- CategoryTheory.Limits.WalkingCospanstatement · cited by 496
- CategoryTheory.Limits.cospanstatement · cited by 467
- CategoryTheory.Limits.PullbackConestatement and proof · cited by 136
- CategoryTheory.Limits.PullbackCone.fststatement and proof · cited by 118
- CategoryTheory.Limits.PullbackCone.sndstatement and proof · cited by 113
- CategoryTheory.Limits.IsLimit.hom_extproof · cited by 43
Cited by11
Results whose statement or proof uses this declaration.
- CategoryTheory.IsPullback.hom_extproof · cited by 16
- CategoryTheory.mono_iff_isIso_fstproof · cited by 2
- CategoryTheory.Limits.CoproductDisjoint.of_cofanproof · cited by 2
- CategoryTheory.Limits.PullbackCone.isIso_fst_of_mono_of_isLimitproof · cited by 2
- CategoryTheory.Functor.relativelyRepresentable.hom_extproof · cited by 2
- CategoryTheory.IsKernelPair.pullbackproof · cited by 0
- CategoryTheory.Limits.PullbackCone.mono_fst_of_is_pullback_of_monoproof · cited by 0
- CategoryTheory.Limits.PullbackCone.mono_snd_of_is_pullback_of_monoproof · cited by 0