Theorems · Theorem · category theory

CategoryTheory.Limits.HasColimitsOfSize.has_colimits_of_shape

∀ {C : Type u} {inst : CategoryTheory.Category.{v, u} C}
  [self : CategoryTheory.Limits.HasColimitsOfSize.{v₁, u₁, v, u} C] (J : Type u₁)
  [inst_1 : CategoryTheory.Category.{v₁, u₁} J], CategoryTheory.Limits.HasColimitsOfShape J C

All F : J ⥤ C have colimits for all small J

Defined in: Mathlib.CategoryTheory.Limits.HasLimits
Cited by: 2 results in Mathlib
Foundations: Depth 2 from the axioms · uses no axioms
Assumes: CategoryTheory.Limits.HasColimitsOfSize CategoryTheory.Category

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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.HasColimitsOfShapestatement · cited by 308
CategoryTheory.Limits.HasColimitsOfSizestatement and proof · cited by 124

Cited by2

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.HasColimitsOfShape.of_smallproof · cited by 1
CategoryTheory.Limits.HasColimits.has_colimits_of_shapeproof · cited by 0