Theorems · Theorem · category theory
CategoryTheory.GrpObj.lift_comp_inv_left
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
{A B : C} [inst_2 : CategoryTheory.GrpObj B] (f : A ⟶ B),
CategoryTheory.CategoryStruct.comp
(CategoryTheory.CartesianMonoidalCategory.lift (CategoryTheory.CategoryStruct.comp f CategoryTheory.GrpObj.inv) f)
CategoryTheory.MonObj.mul =
CategoryTheory.CategoryStruct.comp (CategoryTheory.SemiCartesianMonoidalCategory.toUnit A) CategoryTheory.MonObj.one- Defined in
- Mathlib.CategoryTheory.Monoidal.Grp
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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.MonObj.mulstatement and proof · cited by 230
- CategoryTheory.MonObj.onestatement and proof · cited by 189
- CategoryTheory.CartesianMonoidalCategory.liftstatement and proof · cited by 160
Cited by6
Results whose statement or proof uses this declaration.
- CategoryTheory.GrpObj.eq_lift_inv_rightproof · cited by 3
- CategoryTheory.GrpObj.mul_invproof · cited by 2
- CategoryTheory.GrpObj.inv_homproof · cited by 2
- CategoryTheory.GrpObj.eq_lift_inv_leftproof · cited by 2
- CategoryTheory.GrpObj.isPullbackproof · cited by 1
- CategoryTheory.GrpObj.lift_comp_inv_left_assocproof · cited by 0