Theorems · Theorem · category theory
CategoryTheory.CopyDiscardCategory.discard_tensor
∀ {C : Type u} {inst : CategoryTheory.Category.{v, u} C} {inst_1 : CategoryTheory.MonoidalCategory C}
[self : CategoryTheory.CopyDiscardCategory C] (X Y : C),
CategoryTheory.ComonObj.counit =
CategoryTheory.CategoryStruct.comp
(CategoryTheory.MonoidalCategoryStruct.tensorHom CategoryTheory.ComonObj.counit CategoryTheory.ComonObj.counit)
(CategoryTheory.MonoidalCategoryStruct.leftUnitor (CategoryTheory.MonoidalCategoryStruct.tensorUnit C)).homDiscard distributes over tensor.
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- Foundations
- Depth 4 from the axioms · uses no axioms
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Cites11
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 · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.Iso.homstatement · cited by 7,684
- CategoryTheory.MonoidalCategoryStruct.tensorObjstatement · cited by 3,106
- CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
- CategoryTheory.MonoidalCategoryStruct.tensorUnitstatement · cited by 1,384
- CategoryTheory.MonoidalCategoryStruct.tensorHomstatement · cited by 587
- CategoryTheory.MonoidalCategoryStruct.leftUnitorstatement · cited by 437
- CategoryTheory.ComonObj.counitstatement · cited by 67
- CategoryTheory.CopyDiscardCategorystatement and proof · cited by 6
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