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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.

CategoryTheory.Under.mapComp_eq · cited by 2Under.mapComp_eqCommRingCat.mkUnder_ext · cited by 2CommRingCat.mkUnder_extCategoryTheory.MorphismProperty.ind_iff_exists · cited by 1MorphismProperty.ind_iff_…CategoryTheory.MorphismProperty.ind_iff_ind_underMk · cited by 1MorphismProperty.ind_iff_…CommRingCat.preservesColimit_coyoneda_of_finitePresentation · cited by 1CommRingCat.preservesColi…CommRingCat.preservesLimit_parallelPair_tensorProd_iff_tensorEqualizer_bijective · cited by 1CommRingCat.preservesLimi…CategoryTheory.Under.UnderMorphism.ext_iff · cited by 0UnderMorphism.ext_iffCategoryTheory.Under.mapId_eq · cited by 0Under.mapId_eqCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Functor.map · cited by 8698Functor.mapCategoryTheory.Functor.id · cited by 3333Functor.idCategoryTheory.Discrete · cited by 2447CategoryTheory.DiscreteCategoryTheory.Comma.left · cited by 886Comma.leftCategoryTheory.Functor.fromPUnit · cited by 769Functor.fromPUnitCategoryTheory.Comma.right · cited by 727Comma.rightCategoryTheory.Comma · cited by 566CategoryTheory.CommaCategoryTheory.Comma.hom · cited by 490Comma.homCategoryTheory.Under · cited by 276CategoryTheory.UnderCategoryTheory.Under.right · cited by 128Under.rightCategoryTheory.Under.Hom.right · cited by 67Hom.rightUnderMorphism.extCITED BYCITES

Cites15

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by8

Results whose statement or proof uses this declaration.