Theorems · Theorem · category theory
CategoryTheory.Subobject.isIso_iff_mk_eq_top
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y : C} (f : X ⟶ Y) [inst_1 : CategoryTheory.Mono f],
CategoryTheory.IsIso f ↔ CategoryTheory.Subobject.mk f = ⊤- Defined in
- Mathlib.CategoryTheory.Subobject.Lattice
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Top.topstatement and proof · cited by 9,680
- CategoryTheory.Iso.homproof · cited by 7,684
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- CategoryTheory.Category.comp_idproof · cited by 2,119
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- CategoryTheory.Monostatement and proof · cited by 893
- Eq.leproof · cited by 605
- CategoryTheory.Subobjectstatement · cited by 385
- CategoryTheory.asIsoproof · cited by 177
- CategoryTheory.Subobject.mkstatement and proof · cited by 109
Cited by6
Results whose statement or proof uses this declaration.
- CategoryTheory.ObjectProperty.isStrongGenerator_iffproof · cited by 5
- CategoryTheory.Subobject.isIso_arrow_iff_eq_topproof · cited by 4
- CategoryTheory.Subobject.epi_iff_mk_eq_topproof · cited by 1
- CategoryTheory.Subobject.mk_eq_top_of_isIsoproof · cited by 1
- CategoryTheory.simple_of_isSimpleOrder_subobjectproof · cited by 1