Theorems · Theorem · category theory
CategoryTheory.isIso_iff_of_reflects_iso
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {D : Type u_2}
[inst_1 : CategoryTheory.Category.{v_2, u_2} D] {A B : C} (f : A ⟶ B) (F : CategoryTheory.Functor C D)
[F.ReflectsIsomorphisms], CategoryTheory.IsIso (F.map f) ↔ CategoryTheory.IsIso f- Cited by
- 20 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.Functor.objstatement · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapstatement and proof · cited by 8,698
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- CategoryTheory.Functor.ReflectsIsomorphismsstatement and proof · cited by 82
- CategoryTheory.isIso_of_reflects_isoproof · cited by 19
Cited by20
Results whose statement or proof uses this declaration.
- HomologicalComplex.homotopyEquivalences_extendMap_iffproof · cited by 2
- CategoryTheory.Functor.simple_of_simple_objproof · cited by 2
- AlgebraicGeometry.IsClosedImmersion.isIso_of_ker_eqproof · cited by 2
- CategoryTheory.MonoOver.isIso_iff_isIso_hom_leftproof · cited by 1
- CategoryTheory.GrothendieckTopology.W_sheafToPresheaf_map_iff_isIsoproof · cited by 1
- AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.to_isoproof · cited by 1
- CategoryTheory.Sheaf.isLocallyBijective_iff_isIsoproof · cited by 1
- CategoryTheory.Sheaf.isLocallySurjective_iff_isIsoproof · cited by 1
- CategoryTheory.reflectsIsomorphisms_of_isoproof · cited by 1
- CategoryTheory.Functor.balanced_of_preservesproof · cited by 0