Theorems · Theorem · category theory
CategoryTheory.reflects_epi_of_reflectsColimit
∀ {C : Type u₁} {D : Type u₂} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
(F : CategoryTheory.Functor C D) {X Y : C} (f : X ⟶ Y)
[CategoryTheory.Limits.ReflectsColimit (CategoryTheory.Limits.span f f) F] [CategoryTheory.Epi (F.map f)],
CategoryTheory.Epi fIf F reflects pushouts, then it reflects epimorphisms.
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- Foundations
- Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites18
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- CategoryTheory.Epistatement and proof · cited by 688
- CategoryTheory.Functor.map_idproof · cited by 616
- CategoryTheory.Limits.WalkingSpanstatement · cited by 300
- CategoryTheory.Limits.spanstatement and proof · cited by 294
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