Theorems · Theorem · category theory
CategoryTheory.bijective_iff_isIso_ofHom
∀ {X Y : Type u} (f : X → Y), Function.Bijective f ↔ CategoryTheory.IsIso (TypeCat.ofHom f)- Defined in
- Mathlib.CategoryTheory.Types.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 20 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.IsIsostatement and proof · cited by 1,156
- Function.Bijectivestatement and proof · cited by 863
- TypeCat.ofHomstatement and proof · cited by 389
- CategoryTheory.asIsoproof · cited by 177
- Equiv.bijectiveproof · cited by 132
- Equiv.ofBijectiveproof · cited by 70
- Equiv.toIsoproof · cited by 58
- CategoryTheory.Iso.toEquivproof · cited by 32
Cited by8
Results whose statement or proof uses this declaration.
- CategoryTheory.ConcreteCategory.bijective_of_isIsoproof · cited by 15
- CategoryTheory.ConcreteCategory.isIso_iff_bijectiveproof · cited by 12
- CategoryTheory.isIso_iff_yoneda_map_bijectiveproof · cited by 4
- CategoryTheory.isIso_iff_coyoneda_map_bijectiveproof · cited by 3
- TopCat.Presheaf.app_isIso_of_stalkFunctor_map_isoproof · cited by 2
- CategoryTheory.isIso_iff_isIso_coyoneda_mapproof · cited by 1
- CategoryTheory.isIso_iff_isIso_yoneda_mapproof · cited by 1
- TopCat.GlueData.preimage_image_eq_image'proof · cited by 1