Theorems · Theorem · category theory
CategoryTheory.Limits.BinaryCofan.isColimit_iff_isIso_inl
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} (h : CategoryTheory.Limits.IsInitial Y)
(c : CategoryTheory.Limits.BinaryCofan X Y), Nonempty (CategoryTheory.Limits.IsColimit c) ↔ CategoryTheory.IsIso c.inl- Cited by
- 1 results in Mathlib
- Foundations
- Depth 28 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.
Cites28
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.Homproof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- CategoryTheory.Discretestatement and proof · cited by 2,447
- 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 and proof · cited by 1,319
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.BinaryCofan.isColimit_iff_isIso_inrproof · cited by 2