Theorems · Theorem · category theory

CategoryTheory.AddGrpObj.lift_comp_neg_left

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
  {A B : C} [inst_2 : CategoryTheory.AddGrpObj B] (f : A ⟶ B),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.CartesianMonoidalCategory.lift (CategoryTheory.CategoryStruct.comp f CategoryTheory.AddGrpObj.neg)
        f)
      CategoryTheory.AddMonObj.add =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.SemiCartesianMonoidalCategory.toUnit A)
      CategoryTheory.AddMonObj.zero

Defined in: Mathlib.CategoryTheory.Monoidal.Grp
Cited by: 6 results in Mathlib
Foundations: Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.CartesianMonoidalCategory CategoryTheory.AddGrpObj

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Cites19

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.Category.assocproof · cited by 6,433
CategoryTheory.CategoryStruct.idproof · cited by 6,235
CategoryTheory.MonoidalCategoryStruct.tensorObjstatement · cited by 3,106
CategoryTheory.Category.comp_idproof · cited by 2,119
CategoryTheory.MonoidalCategoryStruct.tensorUnitstatement and proof · cited by 1,384
CategoryTheory.CartesianMonoidalCategorystatement and proof · cited by 947
CategoryTheory.CartesianMonoidalCategory.liftstatement and proof · cited by 160
CategoryTheory.AddMonObj.addstatement and proof · cited by 134
CategoryTheory.SemiCartesianMonoidalCategory.toUnitstatement and proof · cited by 103

Cited by6

Results whose statement or proof uses this declaration.

CategoryTheory.AddGrpObj.eq_lift_neg_rightproof · cited by 3
CategoryTheory.AddGrpObj.eq_lift_neg_leftproof · cited by 2
CategoryTheory.AddGrpObj.neg_homproof · cited by 2
CategoryTheory.AddGrpObj.add_negproof · cited by 2
CategoryTheory.AddGrpObj.isPullbackproof · cited by 1
CategoryTheory.AddGrpObj.lift_comp_neg_left_assocproof · cited by 0