Theorems · Definition · category theory
AddCommGrpCat.free
CategoryTheory.Functor (Type u) AddCommGrpCat
The free functor Type u ⥤ AddCommGroup sending a type X to the
free abelian group with generators x : X.
- Defined in
- Mathlib.Algebra.Category.Grp.Adjunctions
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- AddCommGrpCatstatement · cited by 462
- AddCommGrpCat.ofproof · cited by 97
- FreeAbelianGroupproof · cited by 82
- AddCommGrpCat.ofHomproof · cited by 72
- FreeAbelianGroup.mapproof · cited by 7
Cited by15
Results whose statement or proof uses this declaration.
- CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplexproof · cited by 9
- CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex_fstatement · cited by 1
- CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex_gstatement · cited by 1
- CategoryTheory.GrothendieckTopology.MayerVietorisSquare.isPushoutAddCommGrpFreeSheafstatement and proof · cited by 1
- AddCommGrpCat.free_mapstatement and proof · cited by 0
- AddCommGrpCat.free_map_coestatement · cited by 0
- AddCommGrpCat.free_objstatement and proof · cited by 0
- AddCommGrpCat.free_obj_coestatement · cited by 0
- CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex_X₁statement · cited by 0
- CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex_X₂statement · cited by 0
- CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex_X₃statement · cited by 0
- CategoryTheory.Sheaf.cohomologyPresheafFunctorproof · cited by 0