Mathlib Map

Theorems · Theorem · category theory

CategoryTheory.Limits.hasColimitsOfShape_of_finallySmall

∀ (J : Type u) [inst : CategoryTheory.Category.{v, u} J] [CategoryTheory.FinallySmall J] (C : Type u₁)
  [inst_2 : CategoryTheory.Category.{v₁, u₁} C] [CategoryTheory.Limits.HasColimitsOfSize.{w, w, v₁, u₁} C],
  CategoryTheory.Limits.HasColimitsOfShape J C
Defined in
Mathlib.CategoryTheory.Limits.FinallySmall
Cited by
2 results in Mathlib
Foundations
Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.FinallySmallCategoryTheory.CategoryCategoryTheory.Limits.HasColimitsOfSize
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

PresheafOfModules.colimitAdjunction_homEquiv · cited by 1PresheafOfModules.colimit…PresheafOfModules.colimitAdjunction_homEquiv_symm_apply · cited by 0PresheafOfModules.colimit…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Limits.HasColimitsOfShape · cited by 308Limits.HasColimitsOfShapeCategoryTheory.Limits.HasColimitsOfSize · cited by 124Limits.HasColimitsOfSizeCategoryTheory.FinallySmall · cited by 16CategoryTheory.FinallySma…CategoryTheory.fromFinalModel · cited by 5CategoryTheory.fromFinalM…CategoryTheory.Functor.Final.hasColimitsOfShape_of_final · cited by 2Final.hasColimitsOfShape_…Limits.hasColimitsOfShape_of_…CITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.