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Theorems · Definition · category theory

CategoryTheory.Dial.tensorHomImpl

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasFiniteProducts C] →
      [inst_2 : CategoryTheory.Limits.HasPullbacks C] →
        {X₁ X₂ Y₁ Y₂ : CategoryTheory.Dial C} → (X₁ ⟶ X₂) → (Y₁ ⟶ Y₂) → (X₁.tensorObjImpl Y₁ ⟶ X₂.tensorObjImpl Y₂)

The functorial action of X ⊗ Y in Dial C.

Defined in
Mathlib.CategoryTheory.Dialectica.Monoidal
Cited by
2 results in Mathlib
Foundations
Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasFiniteProductsCategoryTheory.Limits.HasPullbacks
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Around this declaration

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CategoryTheory.Dial.tensorHomImpl_F · cited by 0Dial.tensorHomImpl_FCategoryTheory.Dial.tensorHomImpl_f · cited by 0Dial.tensorHomImpl_fCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Limits.HasPullbacks · cited by 439Limits.HasPullbacksCategoryTheory.Limits.prod.fst · cited by 189prod.fstCategoryTheory.Limits.prod.snd · cited by 185prod.sndCategoryTheory.Limits.HasFiniteProducts · cited by 142Limits.HasFiniteProductsCategoryTheory.Limits.prod.lift · cited by 123prod.liftCategoryTheory.Limits.prod.map · cited by 105prod.mapCategoryTheory.Dial · cited by 80CategoryTheory.DialCategoryTheory.Dial.Hom.f · cited by 35Hom.fCategoryTheory.Dial.tensorObjImpl · cited by 35Dial.tensorObjImplCategoryTheory.Dial.Hom.F · cited by 34Hom.FDial.tensorHomImplCITED BYCITES

Cites13

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Cited by2

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