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Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.tensorHom_id

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.MonoidalCategory C] {X₁ X₂ : C}
  (f : X₁ ⟶ X₂) (Y : C),
  CategoryTheory.MonoidalCategoryStruct.tensorHom f (CategoryTheory.CategoryStruct.id Y) =
    CategoryTheory.MonoidalCategoryStruct.whiskerRight f Y
Defined in
Mathlib.CategoryTheory.Monoidal.Category
Cited by
67 results in Mathlib
Foundations
Depth 5 from the axioms · uses propext
Assumes
CategoryTheory.CategoryCategoryTheory.MonoidalCategory

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.MonoidalCategory.tensor_whiskerLeft · cited by 37MonoidalCategory.tensor_w…CategoryTheory.MonoidalCategory.whiskerRight_tensor · cited by 37MonoidalCategory.whiskerR…CategoryTheory.MonoidalCategory.whisker_assoc · cited by 31MonoidalCategory.whisker_…CategoryTheory.MonoidalCategory.comp_tensor_id · cited by 5MonoidalCategory.comp_ten…CategoryTheory.MonoidalCategory.tensorμ_natural_left · cited by 5MonoidalCategory.tensorμ_…CategoryTheory.MonoidalCategory.tensorμ_natural_right · cited by 5MonoidalCategory.tensorμ_…CategoryTheory.MonoidalCategory.DayConvolution.associator_hom_unit_unit · cited by 4DayConvolution.associator…CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_hom_unit_app · cited by 4DayConvolutionUnit.leftUn…CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_hom_unit_app · cited by 4DayConvolutionUnit.rightU…CategoryTheory.Adjunction.unit_app_tensor_comp_map_δ · cited by 3Adjunction.unit_app_tenso…CategoryTheory.MonoidalCategory.tensor_hom_inv_id · cited by 1MonoidalCategory.tensor_h…CategoryTheory.MonoidalCategory.tensor_hom_inv_id' · cited by 1MonoidalCategory.tensor_h…CategoryTheory.MonoidalCategory.tensor_inv_hom_id · cited by 1MonoidalCategory.tensor_i…CategoryTheory.MonoidalCategory.tensor_inv_hom_id' · cited by 1MonoidalCategory.tensor_i…CategoryTheory.GradedObject.Monoidal.pentagon_inv · cited by 1Monoidal.pentagon_invCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idCategoryTheory.MonoidalCategoryStruct.tensorObj · cited by 3106MonoidalCategoryStruct.te…CategoryTheory.MonoidalCategory · cited by 3095CategoryTheory.MonoidalCa…CategoryTheory.Category.comp_id · cited by 2119Category.comp_idCategoryTheory.MonoidalCategoryStruct.whiskerRight · cited by 903MonoidalCategoryStruct.wh…CategoryTheory.MonoidalCategoryStruct.tensorHom · cited by 587MonoidalCategoryStruct.te…CategoryTheory.MonoidalCategory.tensorHom_def · cited by 58MonoidalCategory.tensorHo…CategoryTheory.MonoidalCategory.whiskerLeft_id · cited by 52MonoidalCategory.whiskerL…MonoidalCategory.tensorHom_idCITED BYCITES

Cites11

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Cited by67

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