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: 3 results in Mathlib
Foundations: Depth 11 from the axioms · uses propext
Assumes: CategoryTheory.Category

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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.IsCoseparatorstatement · cited by 28
CategoryTheory.isCoseparator_defproof · cited by 5

Cited by3

Results whose statement or proof uses this declaration.

CategoryTheory.isCoseparator_iff_of_isLimit_fanproof · cited by 2
CategoryTheory.Preadditive.isCoseparator_iffproof · cited by 1
CategoryTheory.isCoseparator_iff_faithful_yoneda_objproof · cited by 1