Theorems · Theorem · category theory
CategoryTheory.isIso_of_epi_of_strongMono
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {P Q : C} (f : Q ⟶ P) [CategoryTheory.Epi f]
[CategoryTheory.StrongMono f], CategoryTheory.IsIso fA strong monomorphism that is an epimorphism is an isomorphism.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- CategoryTheory.Category.comp_idproof · cited by 2,119
- CategoryTheory.Category.id_compproof · cited by 1,998
- CategoryTheory.IsIsostatement · cited by 1,156
- CategoryTheory.Epistatement and proof · cited by 688
- CategoryTheory.CommSq.liftproof · cited by 34
- CategoryTheory.CommSq.fac_leftproof · cited by 22
- CategoryTheory.CommSq.fac_rightproof · cited by 19
- CategoryTheory.StrongMonostatement and proof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.isIso_of_regularMono_of_epiproof · cited by 0