Theorems · Inductive type · category theory
CategoryTheory.Limits.HasLimitsOfShape
(J : Type u₁) → [CategoryTheory.Category.{v₁, u₁} J] → (C : Type u) → [CategoryTheory.Category.{v, u} C] → PropC has limits of shape J if there exists a limit for every functor F : J ⥤ C.
- Defined in
- Mathlib.CategoryTheory.Limits.HasLimits
- Cited by
- 223 results in Mathlib
- Foundations
- Depth 1 from the axioms, rests on 2 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
Cited by335
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.HasPullbacksproof · cited by 439
- CategoryTheory.Limits.HasTerminalproof · cited by 142
- CategoryTheory.Limits.HasProductsproof · cited by 103
- CategoryTheory.Limits.HasBinaryProductsproof · cited by 79
- CategoryTheory.Limits.limstatement and proof · cited by 70
- CategoryTheory.Limits.HasProductsOfShapeproof · cited by 63
- CategoryTheory.Limits.HasEqualizersproof · cited by 60
- CategoryTheory.Limits.limitObjIsoLimitCompEvaluationstatement and proof · cited by 36
- CategoryTheory.GrothendieckTopology.plusCompIsostatement and proof · cited by 20
- CategoryTheory.Limits.hasLimitsOfShape_of_equivalencestatement and proof · cited by 16
- CategoryTheory.HasExactLimitsOfShapestatement · cited by 13
- CategoryTheory.GrothendieckTopology.sheafifyCompIsostatement and proof · cited by 11
Showing the 200 most cited of 335.