Theorems · Definition · category theory
GrpCat.FilteredColimits.G
{J : Type v} →
[inst : CategoryTheory.SmallCategory J] → [CategoryTheory.IsFiltered J] → CategoryTheory.Functor J GrpCat → MonCatThe colimit of F ⋙ forget₂ GrpCat MonCat in the category MonCat.
In the following, we will show that this has the structure of a group.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.compproof · cited by 6,529
- CategoryTheory.SmallCategorystatement and proof · cited by 480
- CategoryTheory.forget₂proof · cited by 260
- CategoryTheory.IsFilteredstatement and proof · cited by 210
- GrpCatstatement and proof · cited by 146
- MonCatstatement and proof · cited by 127
- MonCat.FilteredColimits.colimitproof · cited by 1
Cited by9
Results whose statement or proof uses this declaration.
- GrpCat.FilteredColimits.G.mkstatement · cited by 5
- GrpCat.FilteredColimits.colimitInvAuxstatement · cited by 1
- GrpCat.FilteredColimits.colimit_mul_mk_eqstatement · cited by 1
- GrpCat.FilteredColimits.G.mk_eqstatement · cited by 1
- GrpCat.FilteredColimits.colimitInvAux_eq_of_relstatement · cited by 0
- GrpCat.FilteredColimits.colimit_inv_mk_eqstatement · cited by 0
- GrpCat.FilteredColimits.colimit_mul_mk_eq'statement · cited by 0
- GrpCat.FilteredColimits.colimit_one_eqstatement · cited by 0
- GrpCat.FilteredColimits.colimitproof · cited by 0