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Theorems · Definition · category theory

CategoryTheory.Dial.leftUnitorImpl

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasFiniteProducts C] →
      [inst_2 : CategoryTheory.Limits.HasPullbacks C] →
        (X : CategoryTheory.Dial C) → CategoryTheory.Dial.tensorUnitImpl.tensorObjImpl X ≅ X

Left unit cancellation 1 ⊗ X ≅ X in Dial C.

Defined in
Mathlib.CategoryTheory.Dialectica.Monoidal
Cited by
4 results in Mathlib
Foundations
Depth 76 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.leftUnitorImpl_hom_F · cited by 0Dial.leftUnitorImpl_hom_FCategoryTheory.Dial.leftUnitorImpl_hom_f · cited by 0Dial.leftUnitorImpl_hom_fCategoryTheory.Dial.leftUnitorImpl_inv_F · cited by 0Dial.leftUnitorImpl_inv_FCategoryTheory.Dial.leftUnitorImpl_inv_f · cited by 0Dial.leftUnitorImpl_inv_fCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Iso · cited by 3963CategoryTheory.IsoCategoryTheory.Limits.HasPullbacks · cited by 439Limits.HasPullbacksCategoryTheory.Limits.HasFiniteProducts · cited by 142Limits.HasFiniteProductsCategoryTheory.Dial · cited by 80CategoryTheory.DialCategoryTheory.Dial.src · cited by 71Dial.srcCategoryTheory.Dial.tgt · cited by 51Dial.tgtCategoryTheory.Dial.tensorObjImpl · cited by 35Dial.tensorObjImplCategoryTheory.Dial.tensorUnitImpl · cited by 19Dial.tensorUnitImplCategoryTheory.Limits.prod.leftUnitor · cited by 7prod.leftUnitorCategoryTheory.Dial.isoMk · cited by 4Dial.isoMkDial.leftUnitorImplCITED BYCITES

Cites11

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Cited by4

Results whose statement or proof uses this declaration.