Theorems · Theorem · category theory
CategoryTheory.GrpObj.lift_inv_comp_right_assoc
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
{A B : C} [inst_2 : CategoryTheory.GrpObj A] [inst_3 : CategoryTheory.GrpObj B] (f : A ⟶ B)
[CategoryTheory.IsMonHom f] {Z : C} (h : B ⟶ Z),
CategoryTheory.CategoryStruct.comp
(CategoryTheory.CartesianMonoidalCategory.lift f (CategoryTheory.CategoryStruct.comp CategoryTheory.GrpObj.inv f))
(CategoryTheory.CategoryStruct.comp CategoryTheory.MonObj.mul h) =
CategoryTheory.CategoryStruct.comp (CategoryTheory.SemiCartesianMonoidalCategory.toUnit A)
(CategoryTheory.CategoryStruct.comp CategoryTheory.MonObj.one h)- Defined in
- Mathlib.CategoryTheory.Monoidal.Grp
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites15
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.MonoidalCategoryStruct.tensorObjstatement · cited by 3,106
- CategoryTheory.MonoidalCategoryStruct.tensorUnitstatement · cited by 1,384
- CategoryTheory.CartesianMonoidalCategorystatement and proof · cited by 947
- CategoryTheory.MonObj.mulstatement and proof · cited by 230
- CategoryTheory.MonObj.onestatement and proof · cited by 189
- CategoryTheory.CartesianMonoidalCategory.liftstatement and proof · cited by 160
- CategoryTheory.SemiCartesianMonoidalCategory.toUnitstatement and proof · cited by 103
- CategoryTheory.GrpObjstatement and proof · cited by 99
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