Theorems · Theorem · category theory
CategoryTheory.Limits.BinaryCofan.isColimit_iff_isIso_inr
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} (h : CategoryTheory.Limits.IsInitial X)
(c : CategoryTheory.Limits.BinaryCofan X Y), Nonempty (CategoryTheory.Limits.IsColimit c) ↔ CategoryTheory.IsIso c.inr- Cited by
- 2 results in Mathlib
- Foundations
- Depth 32 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.
Cites21
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
- CategoryTheory.Functor.objstatement · cited by 19,642
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.Discretestatement · cited by 2,447
- CategoryTheory.Limits.Cocone.ptstatement · cited by 1,354
- CategoryTheory.Limits.WalkingPairstatement · cited by 1,319
- CategoryTheory.Functor.conststatement · cited by 1,264
- CategoryTheory.IsIsostatement · cited by 1,156
- CategoryTheory.Iso.symmproof · cited by 993
- CategoryTheory.Limits.IsColimitstatement and proof · cited by 773
- CategoryTheory.Limits.pairstatement · cited by 536
- Nonempty.someproof · cited by 340
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.BinaryCofan.mono_inr_of_isVanKampenproof · cited by 1
- CategoryTheory.BinaryCofan.isPullback_initial_to_of_isVanKampenproof · cited by 1