Theorems · Theorem · category theory
CategoryTheory.CategoryOfElements.homMk_coe
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {F : CategoryTheory.Functor C (Type w)} (x y : F.Elements)
(f : x.fst ⟶ y.fst) (hf : (CategoryTheory.ConcreteCategory.hom (F.map f)) x.snd = y.snd),
↑(CategoryTheory.CategoryOfElements.homMk x y f hf) = f- Defined in
- Mathlib.CategoryTheory.Elements
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Quot.sound
- Assumes
- CategoryTheory.Category
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapstatement and proof · cited by 8,698
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- TypeCat.Funstatement · cited by 1,307
- CategoryTheory.Functor.Elementsstatement and proof · cited by 141
- CategoryTheory.CategoryOfElements.homMkstatement and proof · cited by 13
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