Theorems · Theorem · category theory

CategoryTheory.ObjectProperty.isStrongGenerator_iff_exists_extremalEpi

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {P : CategoryTheory.ObjectProperty C}
  [CategoryTheory.Limits.HasCoproducts C] [CategoryTheory.LocallySmall.{w, v, u} C]
  [CategoryTheory.ObjectProperty.Small.{w, v, u} P],
  P.IsStrongGenerator ↔ ∀ (X : C), ∃ ι s, ∃ (_ : ∀ (i : ι), P (s i)), ∃ c x p, CategoryTheory.ExtremalEpi p

Defined in

Mathlib.CategoryTheory.Generator.StrongGenerator

Cited by

0 results in Mathlib

Foundations

Depth 49 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasCoproductsCategoryTheory.LocallySmallCategoryTheory.ObjectProperty.Small