Mathlib Map

Theorems · Definition · category theory

AddCommGrpCat.FilteredColimits.colimitCoconeIsColimit

{J : Type v} →
  [inst : CategoryTheory.SmallCategory J] →
    [inst_1 : CategoryTheory.IsFiltered J] →
      (F : CategoryTheory.Functor J AddCommGrpCat) →
        CategoryTheory.Limits.IsColimit (AddCommGrpCat.FilteredColimits.colimitCocone F)

The proposed colimit cocone is a colimit in AddCommGroup.

Defined in
Mathlib.Algebra.Category.Grp.FilteredColimits
Cited by
2 results in Mathlib
Foundations
Depth 48 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.SmallCategoryCategoryTheory.IsFiltered
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

CategoryTheory.Limits.IsColimit.ι_smul · cited by 2IsColimit.ι_smulModuleCat.FilteredColimits.colimitDesc · cited by 2FilteredColimits.colimitD…ModuleCat.FilteredColimits.ι_colimitDesc · cited by 1FilteredColimits.ι_colimi…CategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Functor.comp · cited by 6529Functor.compCategoryTheory.Limits.IsColimit · cited by 773Limits.IsColimitCategoryTheory.SmallCategory · cited by 480CategoryTheory.SmallCateg…AddCommGrpCat · cited by 462AddCommGrpCatCategoryTheory.forget₂ · cited by 260CategoryTheory.forget₂CategoryTheory.IsFiltered · cited by 210CategoryTheory.IsFilteredAddGrpCat · cited by 80AddGrpCatCategoryTheory.Limits.isColimitOfReflects · cited by 19Limits.isColimitOfReflectsAddCommGrpCat.FilteredColimits.colimitCocone · cited by 1FilteredColimits.colimitC…AddGrpCat.FilteredColimits.colimitCoconeIsColimit · cited by 0FilteredColimits.colimitC…FilteredColimits.colimitCocon…CITED BYCITES

Cites11

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

Cited by3

Results whose statement or proof uses this declaration.