Theorems · Theorem · category theory
CategoryTheory.CartesianMonoidalCategory.lift_fst_snd
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
{X Y : C},
CategoryTheory.CartesianMonoidalCategory.lift (CategoryTheory.SemiCartesianMonoidalCategory.fst X Y)
(CategoryTheory.SemiCartesianMonoidalCategory.snd X Y) =
CategoryTheory.CategoryStruct.id (CategoryTheory.MonoidalCategoryStruct.tensorObj X Y)- Cited by
- 10 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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 · cited by 32,603
- CategoryTheory.CategoryStruct.idstatement and proof · cited by 6,235
- CategoryTheory.MonoidalCategoryStruct.tensorObjstatement and proof · cited by 3,106
- CategoryTheory.Category.id_compproof · cited by 1,998
- CategoryTheory.CartesianMonoidalCategorystatement and proof · cited by 947
- CategoryTheory.SemiCartesianMonoidalCategory.fststatement and proof · cited by 184
- CategoryTheory.SemiCartesianMonoidalCategory.sndstatement and proof · cited by 181
- CategoryTheory.CartesianMonoidalCategory.liftstatement and proof · cited by 160
- CategoryTheory.CartesianMonoidalCategory.hom_extproof · cited by 46
- CategoryTheory.CartesianMonoidalCategory.lift_sndproof · cited by 37
- CategoryTheory.CartesianMonoidalCategory.lift_fstproof · cited by 36
Cited by10
Results whose statement or proof uses this declaration.
- CategoryTheory.AddGrpObj.add_negproof · cited by 2
- CategoryTheory.CartesianMonoidalCategory.prodComparison_idproof · cited by 2
- CategoryTheory.GrpObj.mul_invproof · cited by 2
- CategoryTheory.MonObj.mul_eq_mulproof · cited by 1
- CategoryTheory.frobeniusMorphism_mateproof · cited by 1
- CategoryTheory.AddMonObj.add_eq_addproof · cited by 1
- CategoryTheory.GrpObj.ofRepresentableBy_yonedaGrpObjRepresentableByproof · cited by 0
- CategoryTheory.MonObj.ofRepresentableBy_yonedaMonObjRepresentableByproof · cited by 0