Mathlib Map

Theorems · Definition · category theory

CategoryTheory.Deterministic

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.MonoidalCategory C] → [CategoryTheory.CopyDiscardCategory C] → {X Y : C} → (X ⟶ Y) → Prop

A morphism is deterministic if it preserves the comonoid structure. In probabilistic contexts, these are morphisms without randomness.

Defined in
Mathlib.CategoryTheory.CopyDiscardCategory.Deterministic
Cited by
4 results in Mathlib
Foundations
Depth 4 from the axioms · uses no axioms
Assumes
CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.CopyDiscardCategory
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

CategoryTheory.PositiveCategory.noConfusion · cited by 0PositiveCategory.noConfus…CategoryTheory.PositiveCategory.noConfusionType · cited by 0PositiveCategory.noConfus…CategoryTheory.PositiveCategory.recOn · cited by 0PositiveCategory.recOnCategoryTheory.Deterministic.copy_natural · cited by 0Deterministic.copy_naturalCategoryTheory.Deterministic.discard_natural · cited by 0Deterministic.discard_nat…CategoryTheory.PositiveCategory.mk.noConfusion · cited by 0mk.noConfusionCategoryTheory.PositiveCategory.casesOn · cited by 0PositiveCategory.casesOnCategoryTheory.PositiveCategory.copy_comp_natural · cited by 0PositiveCategory.copy_com…SFinKer.deterministic_id_map · cited by 0SFinKer.deterministic_id_…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.MonoidalCategory · cited by 3095CategoryTheory.MonoidalCa…CategoryTheory.IsComonHom · cited by 11CategoryTheory.IsComonHomCategoryTheory.CopyDiscardCategory · cited by 6CategoryTheory.CopyDiscar…CategoryTheory.DeterministicCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by9

Results whose statement or proof uses this declaration.