Theorems · Theorem · category theory

CategoryTheory.MarkovCategory.eq_discard

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.MonoidalCategory C]
  [inst_2 : CategoryTheory.MarkovCategory C] (X : C) (f : X ⟶ CategoryTheory.MonoidalCategoryStruct.tensorUnit C),
  f = CategoryTheory.ComonObj.counit

Any morphism to the unit equals discard.

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

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Cites10

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 and proof · cited by 32,603
CategoryTheory.CategoryStruct.compproof · cited by 17,999
CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
CategoryTheory.Category.comp_idproof · cited by 2,119
CategoryTheory.MonoidalCategoryStruct.tensorUnitstatement and proof · cited by 1,384
CategoryTheory.ComonObj.counitstatement and proof · cited by 67
CategoryTheory.MarkovCategorystatement and proof · cited by 3
CategoryTheory.MarkovCategory.discard_naturalproof · cited by 2
CategoryTheory.CopyDiscardCategory.discard_unitproof · cited by 1

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.MarkovCategory.isTerminalUnitproof · cited by 0