Theorems · Theorem · category theory
CategoryTheory.Limits.BinaryFan.IsLimit.hom_ext
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {W X Y : C} {s : CategoryTheory.Limits.BinaryFan X Y}
(h : CategoryTheory.Limits.IsLimit s) {f g : W ⟶ s.pt},
CategoryTheory.CategoryStruct.comp f s.fst = CategoryTheory.CategoryStruct.comp g s.fst →
CategoryTheory.CategoryStruct.comp f s.snd = CategoryTheory.CategoryStruct.comp g s.snd → f = g- Cited by
- 5 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.
Cites15
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.compstatement and proof · cited by 17,999
- CategoryTheory.Discretestatement and proof · cited by 2,447
- CategoryTheory.Limits.WalkingPairstatement and proof · cited by 1,319
- CategoryTheory.Limits.Cone.ptstatement and proof · cited by 1,298
- CategoryTheory.Limits.IsLimitstatement and proof · cited by 664
- CategoryTheory.Limits.pairstatement · cited by 536
- CategoryTheory.Limits.WalkingPair.casesOnproof · cited by 59
- CategoryTheory.Limits.BinaryFan.sndstatement and proof · cited by 53
- CategoryTheory.Limits.BinaryFan.fststatement and proof · cited by 53
Cited by5
Results whose statement or proof uses this declaration.
- CategoryTheory.CartesianMonoidalCategory.hom_extproof · cited by 46
- CategoryTheory.Limits.biprod.hom_extproof · cited by 34
- CategoryTheory.Limits.prod.hom_extproof · cited by 33
- CategoryTheory.Limits.BinaryFan.isLimit_iff_isIso_fstproof · cited by 1
- CategoryTheory.IsPullback.of_isLimit_binaryFan_of_isTerminalproof · cited by 0