Theorems · Theorem · category theory
CategoryTheory.Functor.splitMonoCategoryImpOfIsEquivalence
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
(F : CategoryTheory.Functor C D) [F.IsEquivalence] [CategoryTheory.SplitMonoCategory C],
CategoryTheory.SplitMonoCategory DIf F : C ⥤ D is an equivalence of categories and C is a SplitMonoCategory,
then D also is.
- Defined in
- Mathlib.CategoryTheory.Functor.EpiMono
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites10
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.Homproof · cited by 32,603
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapproof · cited by 8,698
- CategoryTheory.Monoproof · cited by 893
- CategoryTheory.Functor.IsEquivalencestatement and proof · cited by 111
- CategoryTheory.Functor.invproof · cited by 27
- CategoryTheory.SplitMonoCategorystatement and proof · cited by 3
- CategoryTheory.isSplitMono_of_monoproof · cited by 1
- CategoryTheory.Functor.isSplitMono_iffproof · cited by 1
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