Theorems · Theorem · category theory

CategoryTheory.Deterministic.copy_natural

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.MonoidalCategory C]
  [inst_2 : CategoryTheory.CopyDiscardCategory C] {X Y : C} (f : X ⟶ Y) [CategoryTheory.Deterministic f],
  CategoryTheory.CategoryStruct.comp f CategoryTheory.ComonObj.comul =
    CategoryTheory.CategoryStruct.comp CategoryTheory.ComonObj.comul
      (CategoryTheory.MonoidalCategoryStruct.tensorHom f f)

Deterministic morphisms commute with copying.

Defined in: Mathlib.CategoryTheory.CopyDiscardCategory.Deterministic
Cited by: 0 results in Mathlib
Foundations: Depth 5 from the axioms · uses no axioms
Assumes: CategoryTheory.Category CategoryTheory.MonoidalCategory CategoryTheory.CopyDiscardCategory CategoryTheory.Deterministic

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CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compstatement · cited by 17,999
CategoryTheory.MonoidalCategoryStruct.tensorObjstatement · cited by 3,106
CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
CategoryTheory.MonoidalCategoryStruct.tensorHomstatement · cited by 587
CategoryTheory.ComonObj.comulstatement · cited by 71
CategoryTheory.CopyDiscardCategorystatement and proof · cited by 6
CategoryTheory.Deterministicstatement and proof · cited by 4
CategoryTheory.IsComonHom.hom_comulproof · cited by 4

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