Theorems · Theorem · category theory
CategoryTheory.AddGrpObj.neg_hom
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
{A B : C} [inst_2 : CategoryTheory.AddGrpObj A] [inst_3 : CategoryTheory.AddGrpObj B] (f : A ⟶ B)
[CategoryTheory.IsAddMonHom f],
CategoryTheory.CategoryStruct.comp CategoryTheory.AddGrpObj.neg f =
CategoryTheory.CategoryStruct.comp f CategoryTheory.AddGrpObj.negMorphisms of group objects preserve negations.
- Defined in
- Mathlib.CategoryTheory.Monoidal.Grp
- Cited by
- 2 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.
Cites31
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.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Iso.homproof · cited by 7,684
- CategoryTheory.MonoidalCategoryStruct.tensorObjproof · cited by 3,106
- CategoryTheory.CartesianMonoidalCategorystatement and proof · cited by 947
- CategoryTheory.MonoidalCategoryStruct.whiskerLeftproof · cited by 915
- CategoryTheory.MonoidalCategoryStruct.whiskerRightproof · cited by 903
- CategoryTheory.MonoidalCategoryStruct.associatorproof · cited by 667
- CategoryTheory.SemiCartesianMonoidalCategory.fstproof · cited by 184
- CategoryTheory.SemiCartesianMonoidalCategory.sndproof · cited by 181
- CategoryTheory.CartesianMonoidalCategory.liftproof · cited by 160
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.AddGrpObj.neg_compproof · cited by 2
- CategoryTheory.AddGrpObj.neg_hom_assocproof · cited by 0