Theorems · Theorem · category theory
CategoryTheory.IsIso.of_mono_retraction
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y : C} (f : Y ⟶ X) [hf : CategoryTheory.IsSplitMono f]
[hf' : CategoryTheory.Mono (CategoryTheory.retraction f)], CategoryTheory.IsIso fEvery split mono whose retraction is mono is an iso.
- Defined in
- Mathlib.CategoryTheory.EpiMono
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
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.IsIsostatement · cited by 1,156
- CategoryTheory.Monostatement and proof · cited by 893
- Nonempty.someproof · cited by 340
- CategoryTheory.IsSplitMonostatement and proof · cited by 33
- CategoryTheory.retractionstatement and proof · cited by 14
- CategoryTheory.IsSplitMono.exists_splitMonoproof · cited by 4
- CategoryTheory.IsIso.of_mono_retraction'proof · cited by 1
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