Theorems · Theorem · category theory
CategoryTheory.ObjectProperty.isLocal_iff_isIso
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] (P : CategoryTheory.ObjectProperty C) {X Y : C}
(f : X ⟶ Y), P X → P Y → (P.isLocal f ↔ CategoryTheory.IsIso f)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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.Category.assocproof · cited by 6,433
- 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.ObjectPropertystatement and proof · cited by 798
- CategoryTheory.ObjectProperty.isLocalstatement and proof · cited by 20
- CategoryTheory.ObjectProperty.isLocal_of_isIsoproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.ObjectProperty.isLocal_iff_isIso_mapproof · cited by 2
- CategoryTheory.GrothendieckTopology.W_sheafToPresheaf_map_iff_isIsoproof · cited by 1