Theorems · Theorem · category theory
CategoryTheory.Limits.IsLimit.nonempty_isLimit_iff_isIso_lift
∀ {J : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} J] {C : Type u₃} [inst_1 : CategoryTheory.Category.{v₃, u₃} C]
{F : CategoryTheory.Functor J C} {s t : CategoryTheory.Limits.Cone F} (hs : CategoryTheory.Limits.IsLimit s),
Nonempty (CategoryTheory.Limits.IsLimit t) ↔ CategoryTheory.IsIso (hs.lift t)- Defined in
- Mathlib.CategoryTheory.Limits.IsLimit
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.NatTrans.appproof · cited by 7,406
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.Category.id_compproof · cited by 1,998
- CategoryTheory.Limits.Cone.ptstatement · cited by 1,298
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- CategoryTheory.Limits.Conestatement and proof · cited by 710
- CategoryTheory.Limits.IsLimitstatement and proof · cited by 664
- CategoryTheory.Limits.Cone.πproof · cited by 500
- CategoryTheory.Limits.IsLimit.liftstatement and proof · cited by 167
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.Fan.nonempty_isLimit_iff_isIso_piLiftproof · cited by 0