Theorems · Theorem · category theory
Stonean.epi_iff_surjective
∀ {X Y : Stonean} (f : X ⟶ Y), CategoryTheory.Epi f ↔ Function.Surjective ⇑(CategoryTheory.ConcreteCategory.hom f)A morphism in Stonean is an epi iff it is surjective.
- Defined in
- Mathlib.Topology.Category.Stonean.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites44
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setproof · cited by 53,352
- CategoryTheory.Categoryproof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- Set.ofPredproof · cited by 6,101
- nhdsproof · cited by 5,554
- Set.rangeproof · cited by 4,705
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- Compl.complproof · cited by 2,925
- FunLikeproof · cited by 2,560
Cited by1
Results whose statement or proof uses this declaration.
- Stonean.effectiveEpi_tfaeproof · cited by 1