Theorems · Theorem · category theory

CategoryTheory.isCoseparator_def

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

Defined in: Mathlib.CategoryTheory.Generator.Basic
Cited by: 5 results in Mathlib
Foundations: Depth 10 from the axioms · uses propext
Assumes: CategoryTheory.Category

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Cites6

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.compstatement and proof · cited by 17,999
CategoryTheory.IsCoseparatorstatement and proof · cited by 28
CategoryTheory.ObjectProperty.singletonproof · cited by 20
CategoryTheory.ObjectProperty.singleton_iffproof · cited by 4

Cited by5

Results whose statement or proof uses this declaration.

CategoryTheory.IsCoseparator.defproof · cited by 3
CategoryTheory.Preadditive.isCoseparator_iffproof · cited by 1
CategoryTheory.isCoseparator_iff_faithful_yoneda_objproof · cited by 1
CategoryTheory.isCoseparator_of_isLimit_fanproof · cited by 1
CategoryTheory.isCoseparator_iff_monoproof · cited by 0