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Theorems · Definition · category theory

CategoryTheory.Dial.tensorObjImpl

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasFiniteProducts C] →
      [CategoryTheory.Limits.HasPullbacks C] → CategoryTheory.Dial C → CategoryTheory.Dial C → CategoryTheory.Dial C

The object X ⊗ Y in the Dial C category just tuples the left and right components.

Defined in
Mathlib.CategoryTheory.Dialectica.Monoidal
Cited by
35 results in Mathlib
Foundations
Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasFiniteProductsCategoryTheory.Limits.HasPullbacks
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Around this declaration

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

CategoryTheory.Dial.whiskerLeft_F · cited by 4Dial.whiskerLeft_FCategoryTheory.Dial.whiskerRight_F · cited by 4Dial.whiskerRight_FCategoryTheory.Dial.associatorImpl · cited by 4Dial.associatorImplCategoryTheory.Dial.associator_hom_F · cited by 4Dial.associator_hom_FCategoryTheory.Dial.leftUnitorImpl · cited by 4Dial.leftUnitorImplCategoryTheory.Dial.rightUnitorImpl · cited by 4Dial.rightUnitorImplCategoryTheory.Dial.leftUnitor_hom_F · cited by 2Dial.leftUnitor_hom_FCategoryTheory.Dial.rightUnitor_hom_F · cited by 2Dial.rightUnitor_hom_FCategoryTheory.Dial.tensorHomImpl · cited by 2Dial.tensorHomImplCategoryTheory.Dial.associator_inv_F · cited by 1Dial.associator_inv_FCategoryTheory.Dial.whiskerLeft_f · cited by 0Dial.whiskerLeft_fCategoryTheory.Dial.whiskerRight_f · cited by 0Dial.whiskerRight_fCategoryTheory.Dial.associatorImpl_hom_F · cited by 0Dial.associatorImpl_hom_FCategoryTheory.Dial.associatorImpl_hom_f · cited by 0Dial.associatorImpl_hom_fCategoryTheory.Dial.associatorImpl_inv_F · cited by 0Dial.associatorImpl_inv_FCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Limits.HasPullbacks · cited by 439Limits.HasPullbacksCategoryTheory.Limits.prod · cited by 364Limits.prodCategoryTheory.Limits.prod.fst · cited by 189prod.fstCategoryTheory.Limits.prod.snd · cited by 185prod.sndCategoryTheory.Limits.HasFiniteProducts · cited by 142Limits.HasFiniteProductsCategoryTheory.Limits.prod.map · cited by 105prod.mapCategoryTheory.Dial · cited by 80CategoryTheory.DialCategoryTheory.Dial.src · cited by 71Dial.srcCategoryTheory.Subobject.pullback · cited by 54Subobject.pullbackCategoryTheory.Dial.tgt · cited by 51Dial.tgtCategoryTheory.Dial.rel · cited by 15Dial.relDial.tensorObjImplCITED BYCITES

Cites13

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Cited by39

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