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Theorems · Theorem · category theory

CategoryTheory.isIso_of_regularMono_of_epi

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y : C} (f : X ⟶ Y) (h : CategoryTheory.RegularMono f)
  [CategoryTheory.Epi f], CategoryTheory.IsIso f

A regular monomorphism is an isomorphism if it is an epimorphism.

Defined in
Mathlib.CategoryTheory.Limits.Shapes.RegularMono
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Foundations
Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Epi
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CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.IsIso · cited by 1156CategoryTheory.IsIsoCategoryTheory.Epi · cited by 688CategoryTheory.EpiCategoryTheory.RegularMono · cited by 14CategoryTheory.RegularMonoCategoryTheory.StrongMono · cited by 11CategoryTheory.StrongMonoCategoryTheory.isIso_of_epi_of_strongMono · cited by 1CategoryTheory.isIso_of_e…CategoryTheory.RegularMono.strongMono · cited by 1RegularMono.strongMonoCategoryTheory.isIso_of_regul…CITED BYCITES

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