Theorems · Theorem · category theory

CategoryTheory.ObjectProperty.isStrongGenerator_iff

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {P : CategoryTheory.ObjectProperty C},
  P.IsStrongGenerator ↔
    P.IsSeparating ∧
      ∀ ⦃X Y : C⦄ (i : X ⟶ Y) [CategoryTheory.Mono i],
        (∀ (G : C), P G → Function.Surjective fun f => CategoryTheory.CategoryStruct.comp f i) → CategoryTheory.IsIso i

Defined in

Mathlib.CategoryTheory.Generator.StrongGenerator

Cited by

5 results in Mathlib

Foundations

Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category