Theorems · Theorem · category theory
CategoryTheory.AddGrpObj.comp_neg
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
{G X Y : C} [inst_2 : CategoryTheory.AddGrpObj G] (f : X ⟶ Y) (g : Y ⟶ G),
CategoryTheory.CategoryStruct.comp f (-g) = -CategoryTheory.CategoryStruct.comp f g- Cited by
- 9 results in Mathlib
- Foundations
- Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objproof · cited by 19,642
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.Functor.mapproof · cited by 8,698
- Quiver.Hom.opproof · cited by 1,948
- CategoryTheory.CartesianMonoidalCategorystatement and proof · cited by 947
- CategoryTheory.AddGrpObjstatement and proof · cited by 88
- CategoryTheory.Hom.addGroupstatement · cited by 25
- AddMonoidHom.map_negproof · cited by 22
- AddGrpCat.Hom.homproof · cited by 20
- CategoryTheory.yonedaAddGrpproof · cited by 7
Cited by9
Results whose statement or proof uses this declaration.
- CategoryTheory.AddGrpObj.lift_addCommutator_eq_add_add_neg_negproof · cited by 2
- CategoryTheory.AddGrpObj.lift_addConj_eq_add_add_negproof · cited by 2
- CategoryTheory.AddGrpObj.whiskerLeft_η_addCommutatorproof · cited by 1
- CategoryTheory.AddGrpObj.zero_negproof · cited by 1
- CategoryTheory.AddGrpObj.η_whiskerRight_addCommutatorproof · cited by 1
- CategoryTheory.AddGrpObj.comp_zsmulproof · cited by 1
- CategoryTheory.IsAddMonHom.Normal.of_isPullback_ηproof · cited by 0
- CategoryTheory.AddGrpObj.comp_neg_assocproof · cited by 0
- CategoryTheory.IsAddMonHom.normal_iff_normal_addMonoidHomproof · cited by 0