Theorems · Theorem · category theory
CategoryTheory.Abelian.mono_inr_of_isColimit
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [CategoryTheory.Abelian C]
[CategoryTheory.Limits.HasPushouts C] {X Y Z : C} (f : X ⟶ Y) (g : X ⟶ Z) [CategoryTheory.Mono f]
{s : CategoryTheory.Limits.PushoutCocone f g} (hs : CategoryTheory.Limits.IsColimit s), CategoryTheory.Mono s.inr- Defined in
- Mathlib.CategoryTheory.Abelian.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites20
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.NatTrans.appproof · cited by 7,406
- CategoryTheory.Abelianstatement and proof · cited by 1,753
- CategoryTheory.Limits.Cocone.ptstatement · cited by 1,354
- CategoryTheory.Limits.WalkingPairstatement · cited by 1,319
- CategoryTheory.Monostatement and proof · cited by 893
- CategoryTheory.Limits.IsColimitstatement and proof · cited by 773
- CategoryTheory.Limits.Cocone.ιproof · cited by 605
- CategoryTheory.Limits.WalkingSpanstatement · cited by 300
- CategoryTheory.Limits.spanstatement and proof · cited by 294
- CategoryTheory.Limits.colimit.isColimitproof · cited by 193
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