Theorems · Theorem · category theory
CategoryTheory.Subobject.epi_iff_mk_eq_top
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y : C} [CategoryTheory.Balanced C] (f : X ⟶ Y)
[inst_2 : CategoryTheory.Mono f], CategoryTheory.Epi f ↔ CategoryTheory.Subobject.mk f = ⊤- Defined in
- Mathlib.CategoryTheory.Subobject.Lattice
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Top.topstatement · cited by 9,680
- CategoryTheory.IsIsoproof · cited by 1,156
- CategoryTheory.Monostatement and proof · cited by 893
- CategoryTheory.Epistatement and proof · cited by 688
- CategoryTheory.Subobjectstatement · cited by 385
- CategoryTheory.Subobject.mkstatement · cited by 109
- CategoryTheory.Balancedstatement and proof · cited by 61
- CategoryTheory.isIso_of_mono_of_epiproof · cited by 24
- CategoryTheory.Subobject.isIso_iff_mk_eq_topproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.