Theorems · Theorem · category theory
CategoryTheory.CartesianMonoidalCategory.comp_lift
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
{V W X Y : C} (f : V ⟶ W) (g : W ⟶ X) (h : W ⟶ Y),
CategoryTheory.CategoryStruct.comp f (CategoryTheory.CartesianMonoidalCategory.lift g h) =
CategoryTheory.CartesianMonoidalCategory.lift (CategoryTheory.CategoryStruct.comp f g)
(CategoryTheory.CategoryStruct.comp f h)- Cited by
- 13 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 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.CartesianMonoidalCategorystatement and proof · cited by 947
- CategoryTheory.SemiCartesianMonoidalCategory.fstproof · cited by 184
- CategoryTheory.SemiCartesianMonoidalCategory.sndproof · 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 by13
Results whose statement or proof uses this declaration.
- CategoryTheory.CartesianMonoidalCategory.comp_lift_assocproof · cited by 7
- CategoryTheory.CartesianMonoidalCategory.prodComparison_compproof · cited by 3
- CategoryTheory.AddGrpObj.add_negproof · cited by 2
- CategoryTheory.GrpObj.mul_invproof · cited by 2
- CategoryTheory.add_mul_iffproof · cited by 1
- CategoryTheory.frobeniusMorphism_mateproof · cited by 1
- CategoryTheory.mul_add_iffproof · cited by 1
- CategoryTheory.ModObj.lift_leftSMul_eq_lift_iffproof · cited by 0
- CategoryTheory.IsSifted.factorization_prodComparison_colimproof · cited by 0
- CategoryTheory.CartesianMonoidalCategory.prodComparisonIso_compproof · cited by 0
- SSet.finite_of_isPullbackproof · cited by 0