Theorems · Inductive type · category theory
CategoryTheory.Limits.IsLimit
{J : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} J] →
{C : Type u₃} →
[inst_1 : CategoryTheory.Category.{v₃, u₃} C] →
{F : CategoryTheory.Functor J C} → CategoryTheory.Limits.Cone F → Type (max (max u₁ u₃) v₃)A cone t on F is a limit cone if each cone on F admits a unique
cone morphism to t.
- Defined in
- Mathlib.CategoryTheory.Limits.IsLimit
- Cited by
- 664 results in Mathlib
- Foundations
- Depth 3 from the axioms, rests on 4 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.Limits.Conestatement · cited by 710
Cited by1,416
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.IsLimit.liftstatement and proof · cited by 167
- CategoryTheory.Limits.IsTerminalproof · cited by 153
- CategoryTheory.Limits.limit.isLimitstatement · cited by 146
- CategoryTheory.Limits.isLimitOfPreservesstatement and proof · cited by 76
- CategoryTheory.Limits.IsLimit.facstatement and proof · cited by 67
- CategoryTheory.Limits.LimitCone.isLimitstatement · cited by 58
- CategoryTheory.Limits.IsLimit.conePointUniqueUpToIsostatement and proof · cited by 57
- CategoryTheory.IsPullback.isLimitstatement · cited by 47
- CategoryTheory.Limits.IsLimit.hom_extstatement and proof · cited by 43
- CategoryTheory.Limits.IsLimit.ofIsoLimitstatement and proof · cited by 39
- CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_inv_compstatement and proof · cited by 37
- CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_hom_compstatement and proof · cited by 33
Showing the 200 most cited of 1,416.