Theorems · Theorem · category theory

CategoryTheory.ObjectProperty.IsStrongGenerator.isIso_of_mono

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {P : CategoryTheory.ObjectProperty C},
  P.IsStrongGenerator →
    ∀ ⦃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: 3 results in Mathlib
Foundations: Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Mono

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

Cites8

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.IsIsostatement · cited by 1,156
CategoryTheory.Monostatement and proof · cited by 893
CategoryTheory.ObjectPropertystatement and proof · cited by 798
CategoryTheory.ObjectProperty.IsStrongGeneratorstatement and proof · cited by 18
CategoryTheory.ObjectProperty.isStrongGenerator_iffproof · cited by 5

Cited by3

Results whose statement or proof uses this declaration.

CategoryTheory.ObjectProperty.IsStrongGenerator.isDense_colimitsCardinalClosure_ιproof · cited by 2
CategoryTheory.ObjectProperty.IsStrongGenerator.extremalEpi_coproductFromproof · cited by 1
CategoryTheory.ObjectProperty.IsStrongGenerator.exists_of_mono_not_isIsoproof · cited by 0