Theorems · Theorem · category theory
CategoryTheory.Under.UnderMorphism.ext
∀ {T : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} T] {X : T} {U V : CategoryTheory.Under X} {f g : U ⟶ V},
CategoryTheory.Under.Hom.right f = CategoryTheory.Under.Hom.right g → f = g- Defined in
- Mathlib.CategoryTheory.Comma.Over.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 29 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.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Functorproof · cited by 16,252
- CategoryTheory.Functor.mapproof · cited by 8,698
- CategoryTheory.Functor.idproof · cited by 3,333
- CategoryTheory.Discreteproof · cited by 2,447
- CategoryTheory.Comma.leftproof · cited by 886
- CategoryTheory.Functor.fromPUnitproof · cited by 769
- CategoryTheory.Comma.rightproof · cited by 727
- CategoryTheory.Commaproof · cited by 566
- CategoryTheory.Comma.homproof · cited by 490
Cited by8
Results whose statement or proof uses this declaration.
- CategoryTheory.Under.mapComp_eqproof · cited by 2
- CommRingCat.mkUnder_extproof · cited by 2
- CategoryTheory.MorphismProperty.ind_iff_existsproof · cited by 1
- CategoryTheory.MorphismProperty.ind_iff_ind_underMkproof · cited by 1
- CommRingCat.preservesColimit_coyoneda_of_finitePresentationproof · cited by 1
- CategoryTheory.Under.UnderMorphism.ext_iffproof · cited by 0
- CategoryTheory.Under.mapId_eqproof · cited by 0