Theorems · Theorem · category theory
CategoryTheory.IsIso.of_epi_section
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y : C} (f : X ⟶ Y) [hf : CategoryTheory.IsSplitEpi f]
[hf' : CategoryTheory.Epi (CategoryTheory.section_ f)], CategoryTheory.IsIso fEvery split epi whose section is epi is an iso.
- Defined in
- Mathlib.CategoryTheory.EpiMono
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 8 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.Epistatement and proof · cited by 688
- Nonempty.someproof · cited by 340
- CategoryTheory.IsSplitEpistatement and proof · cited by 46
- CategoryTheory.section_statement and proof · cited by 21
- CategoryTheory.IsSplitEpi.exists_splitEpiproof · cited by 4
- CategoryTheory.IsIso.of_epi_section'proof · cited by 3
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