Theorems · Theorem · category theory
CategoryTheory.epi_iff_isIso_inl
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {X Y : C} {f : X ⟶ Y}
{c : CategoryTheory.Limits.PushoutCocone f f} (hc : CategoryTheory.Limits.IsColimit c),
CategoryTheory.Epi f ↔ CategoryTheory.IsIso c.inl- Defined in
- Mathlib.CategoryTheory.Limits.EpiMono
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 29 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.
Cites23
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.Limits.Cocone.ptstatement and proof · cited by 1,354
- CategoryTheory.Limits.WalkingPairstatement · cited by 1,319
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- CategoryTheory.Limits.IsColimitstatement and proof · cited by 773
- CategoryTheory.Epistatement · cited by 688
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.JointlyReflectIsomorphisms.epiproof · cited by 1
- CategoryTheory.epi_iff_isIso_inrproof · cited by 0