Theorems · Theorem · category theory

CategoryTheory.IsCodetector.def

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

Defined in: Mathlib.CategoryTheory.Generator.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 11 from the axioms · uses propext
Assumes: CategoryTheory.Category

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Cites7

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.IsIsostatement · cited by 1,156
ExistsUniquestatement · cited by 268
CategoryTheory.IsCodetectorstatement · cited by 14
CategoryTheory.isCodetector_defproof · cited by 2

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.isCodetector_iff_reflectsIsomorphisms_yoneda_objproof · cited by 0