Theorems · Theorem · category theory
CategoryTheory.CartesianMonoidalCategory.tensorHom_snd
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
{X₁ X₂ Y₁ Y₂ : C} (f : X₁ ⟶ X₂) (g : Y₁ ⟶ Y₂),
CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.tensorHom f g)
(CategoryTheory.SemiCartesianMonoidalCategory.snd X₂ Y₂) =
CategoryTheory.CategoryStruct.comp (CategoryTheory.SemiCartesianMonoidalCategory.snd X₁ Y₁) g- Cited by
- 12 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.
Cites13
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.MonoidalCategoryStruct.whiskerLeftproof · cited by 915
- CategoryTheory.MonoidalCategoryStruct.whiskerRightproof · cited by 903
- CategoryTheory.MonoidalCategoryStruct.tensorHomstatement · cited by 587
- CategoryTheory.SemiCartesianMonoidalCategory.sndstatement and proof · cited by 181
- CategoryTheory.MonoidalCategory.tensorHom_defproof · cited by 58
- CategoryTheory.CartesianMonoidalCategory.whiskerLeft_sndproof · cited by 19
Cited by12
Results whose statement or proof uses this declaration.
- CategoryTheory.CartesianMonoidalCategory.lift_mapproof · cited by 3
- CategoryTheory.CartesianMonoidalCategory.prodComparison_naturalproof · cited by 2
- CategoryTheory.CartesianMonoidalCategory.tensorδ_fstproof · cited by 1
- CategoryTheory.CartesianMonoidalCategory.tensorδ_sndproof · cited by 1
- CategoryTheory.CartesianMonoidalCategory.tensorμ_fstproof · cited by 1
- CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left_sndproof · cited by 1
- CategoryTheory.CartesianMonoidalCategory.tensorμ_sndproof · cited by 1
- CategoryTheory.bijection_symm_apply_idproof · cited by 1
- CategoryTheory.CartesianMonoidalCategory.lift_fst_comp_snd_compproof · cited by 1
- CategoryTheory.CartesianMonoidalCategory.lift_snd_comp_fst_compproof · cited by 1
- CategoryTheory.CartesianMonoidalCategory.tensorHom_snd_assocproof · cited by 0
- CategoryTheory.Functor.Monoidal.tensorHom_app_sndproof · cited by 0