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Theorems · Definition · category theory

GrpCat.FilteredColimits.colimitInvAux

{J : Type v} →
  [inst : CategoryTheory.SmallCategory J] →
    [inst_1 : CategoryTheory.IsFiltered J] →
      (F : CategoryTheory.Functor J GrpCat) → (j : J) × ↑(F.obj j) → ↑(GrpCat.FilteredColimits.G F)

The "unlifted" version of taking inverses in the colimit.

Defined in
Mathlib.Algebra.Category.Grp.FilteredColimits
Cited by
1 results in Mathlib
Foundations
Depth 36 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.

GrpCat.FilteredColimits.colimitInvAux_eq_of_rel · cited by 0FilteredColimits.colimitI…CategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.SmallCategory · cited by 480CategoryTheory.SmallCateg…CategoryTheory.IsFiltered · cited by 210CategoryTheory.IsFilteredGrpCat · cited by 146GrpCatGrpCat.carrier · cited by 125GrpCat.carrierMonCat.carrier · cited by 107MonCat.carrierGrpCat.FilteredColimits.G · cited by 6FilteredColimits.GGrpCat.FilteredColimits.G.mk · cited by 5G.mkFilteredColimits.colimitInvAuxCITED BYCITES

Cites9

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

Cited by1

Results whose statement or proof uses this declaration.