Theorems · Definition · category theory

CategoryTheory.CommComon.trivial

(C : Type u₁) →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    [inst_1 : CategoryTheory.MonoidalCategory C] →
      [inst_2 : CategoryTheory.BraidedCategory C] → CategoryTheory.CommComon C

The trivial commutative comonoid object. We later show this is initial in CommComon C.

Defined in: Mathlib.CategoryTheory.Monoidal.CommComon_
Cited by: 3 results in Mathlib
Foundations: Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.MonoidalCategory CategoryTheory.BraidedCategory

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Cites5

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
CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
CategoryTheory.MonoidalCategoryStruct.tensorUnitproof · cited by 1,384
CategoryTheory.BraidedCategorystatement and proof · cited by 779
CategoryTheory.CommComonstatement · cited by 11

Cited by3

Results whose statement or proof uses this declaration.

CategoryTheory.CommComon.trivial_comon_comulstatement · cited by 0
CategoryTheory.CommComon.trivial_comon_counitstatement · cited by 0
CategoryTheory.CommComon.trivial_Xstatement and proof · cited by 0