Theorems · Theorem · category theory

CategoryTheory.IsSeparator.def

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {G : C},
  CategoryTheory.IsSeparator G →
    ∀ ⦃X Y : C⦄ (f g : X ⟶ Y),
      (∀ (h : G ⟶ X), CategoryTheory.CategoryStruct.comp h f = CategoryTheory.CategoryStruct.comp h g) → f = g

Defined in: Mathlib.CategoryTheory.Generator.Basic
Cited by: 3 results in Mathlib
Foundations: Depth 11 from the axioms · uses propext
Assumes: CategoryTheory.Category

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites5

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 · cited by 32,603
CategoryTheory.CategoryStruct.compstatement · cited by 17,999
CategoryTheory.IsSeparatorstatement · cited by 58
CategoryTheory.isSeparator_defproof · cited by 5

Cited by3

Results whose statement or proof uses this declaration.

CategoryTheory.isSeparator_iff_of_isColimit_cofanproof · cited by 2
CategoryTheory.Preadditive.isSeparator_iffproof · cited by 2
CategoryTheory.isSeparator_iff_faithful_coyoneda_objproof · cited by 1