Theorems · Theorem · category theory
CategoryTheory.ObjectProperty.IsStrongGenerator.mk_of_exists_extremalEpi
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {P : CategoryTheory.ObjectProperty C},
(∀ (X : C), ∃ ι s, ∃ (_ : ∀ (i : ι), P (s i)), ∃ c x p, CategoryTheory.ExtremalEpi p) → P.IsStrongGenerator- Cited by
- 1 results in Mathlib
- Foundations
- Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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.compproof · cited by 17,999
- CategoryTheory.Discretestatement · cited by 2,447
- CategoryTheory.Limits.Cocone.ptstatement and proof · cited by 1,354
- CategoryTheory.Monoproof · cited by 893
- CategoryTheory.ObjectPropertystatement and proof · cited by 798
- CategoryTheory.Limits.IsColimitstatement and proof · cited by 773
- CategoryTheory.Discrete.functorstatement · cited by 633
- CategoryTheory.Limits.Cofan.injproof · cited by 170
- CategoryTheory.Limits.Cofanstatement and proof · cited by 124
- CategoryTheory.Limits.Cofan.IsColimit.descproof · cited by 24
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.ObjectProperty.isStrongGenerator_iff_exists_extremalEpiproof · cited by 0