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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
Defined in
Mathlib.CategoryTheory.Monoidal.Cartesian.Grp
Cited by
9 results in Mathlib
Foundations
Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.AddGrpObj

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.AddGrpObj.lift_addCommutator_eq_add_add_neg_neg · cited by 2AddGrpObj.lift_addCommuta…CategoryTheory.AddGrpObj.lift_addConj_eq_add_add_neg · cited by 2AddGrpObj.lift_addConj_eq…CategoryTheory.AddGrpObj.whiskerLeft_η_addCommutator · cited by 1AddGrpObj.whiskerLeft_η_a…CategoryTheory.AddGrpObj.zero_neg · cited by 1AddGrpObj.zero_negCategoryTheory.AddGrpObj.η_whiskerRight_addCommutator · cited by 1AddGrpObj.η_whiskerRight_…CategoryTheory.AddGrpObj.comp_zsmul · cited by 1AddGrpObj.comp_zsmulCategoryTheory.IsAddMonHom.Normal.of_isPullback_η · cited by 0Normal.of_isPullback_ηCategoryTheory.AddGrpObj.comp_neg_assoc · cited by 0AddGrpObj.comp_neg_assocCategoryTheory.IsAddMonHom.normal_iff_normal_addMonoidHom · cited by 0IsAddMonHom.normal_iff_no…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Functor.map · cited by 8698Functor.mapQuiver.Hom.op · cited by 1948Hom.opCategoryTheory.CartesianMonoidalCategory · cited by 947CategoryTheory.CartesianM…CategoryTheory.AddGrpObj · cited by 88CategoryTheory.AddGrpObjCategoryTheory.Hom.addGroup · cited by 25Hom.addGroupAddMonoidHom.map_neg · cited by 22AddMonoidHom.map_negAddGrpCat.Hom.hom · cited by 20Hom.homCategoryTheory.yonedaAddGrp · cited by 7CategoryTheory.yonedaAddG…AddGrpObj.comp_negCITED BYCITES

Cites12

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Cited by9

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