Theorems · Theorem · category theory
CategoryTheory.Limits.HasLimitsOfSize.has_limits_of_shape
∀ {C : Type u} {inst : CategoryTheory.Category.{v, u} C} [self : CategoryTheory.Limits.HasLimitsOfSize.{v₁, u₁, v, u} C]
(J : Type u₁) [inst_1 : CategoryTheory.Category.{v₁, u₁} J], CategoryTheory.Limits.HasLimitsOfShape J CAll functors F : J ⥤ C from all small J have limits
- Defined in
- Mathlib.CategoryTheory.Limits.HasLimits
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 2 from the axioms · 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 and proof · cited by 32,673
- CategoryTheory.Limits.HasLimitsOfShapestatement · cited by 223
- CategoryTheory.Limits.HasLimitsOfSizestatement and proof · cited by 71
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.HasLimitsOfShape.of_smallproof · cited by 1
- CategoryTheory.Limits.HasLimits.has_limits_of_shapeproof · cited by 0