Theorems · Definition · category theory
CategoryTheory.Subobject.isoOfMkEqMk
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
{B A₁ A₂ : C} →
(f : A₁ ⟶ B) →
(g : A₂ ⟶ B) →
[inst_1 : CategoryTheory.Mono f] →
[inst_2 : CategoryTheory.Mono g] → CategoryTheory.Subobject.mk f = CategoryTheory.Subobject.mk g → (A₁ ≅ A₂)An equality of subobjects gives an isomorphism of the corresponding objects.
- Defined in
- Mathlib.CategoryTheory.Subobject.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.Isostatement · cited by 3,963
- CategoryTheory.Monostatement and proof · cited by 893
- CategoryTheory.Subobjectstatement · cited by 385
- CategoryTheory.Subobject.mkstatement and proof · cited by 109
- CategoryTheory.Subobject.ofMkLEMkproof · cited by 18
Cited by8
Results whose statement or proof uses this declaration.
- CategoryTheory.Subobject.isIso_iff_mk_eq_topproof · cited by 6
- CategoryTheory.Subobject.map_obj_injectiveproof · cited by 3
- CategoryTheory.Subobject.isoOfMkEqMk_homstatement and proof · cited by 2
- CategoryTheory.Subobject.mk_lt_mk_of_commproof · cited by 2
- CategoryTheory.Subobject.nontrivial_of_not_isZeroproof · cited by 1
- CategoryTheory.Subobject.isoOfMkEqMk_invstatement and proof · cited by 0
- CategoryTheory.Subobject.isoOfMkEqMk.congr_simpstatement and proof · cited by 0