Theorems · Definition · category theory
CategoryTheory.Preadditive.toCommGrp
(C : Type u) →
[inst : CategoryTheory.Category.{v, u} C] →
[CategoryTheory.Preadditive C] →
[inst_2 : CategoryTheory.CartesianMonoidalCategory C] →
[inst_3 : CategoryTheory.BraidedCategory C] → CategoryTheory.Functor C (CategoryTheory.CommGrp C)The canonical functor from an additive category into its commutative group objects. This is
always an equivalence, see commGrpEquivalence.
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 36 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.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- CategoryTheory.CartesianMonoidalCategorystatement and proof · cited by 947
- CategoryTheory.BraidedCategorystatement and proof · cited by 779
- CategoryTheory.CommGrpstatement · cited by 74
- CategoryTheory.InducedCategory.homMkproof · cited by 33
- CategoryTheory.Grp.homMk''proof · cited by 4
Cited by9
Results whose statement or proof uses this declaration.
- CategoryTheory.Preadditive.commGrpEquivalenceproof · cited by 11
- CategoryTheory.Preadditive.commGrpEquivalenceAuxstatement and proof · cited by 2
- CategoryTheory.Preadditive.commGrpEquivalenceAux_hom_app_hom_hom_homstatement · cited by 0
- CategoryTheory.Preadditive.commGrpEquivalenceAux_inv_app_hom_hom_homstatement · cited by 0
- CategoryTheory.Preadditive.commGrpEquivalence_counitIso_hom_app_hom_hom_homstatement · cited by 0
- CategoryTheory.Preadditive.commGrpEquivalence_counitIso_inv_app_hom_hom_homstatement · cited by 0
- CategoryTheory.Preadditive.toCommGrp_mapstatement and proof · cited by 0
- CategoryTheory.Preadditive.toCommGrp_obj_Xstatement and proof · cited by 0
- CategoryTheory.Preadditive.toCommGrp_obj_grpstatement and proof · cited by 0