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Theorems · Definition · category theory

CategoryTheory.Bicategory.Comonad

{B : Type u} → [inst : CategoryTheory.Bicategory B] → {a : B} → (a ⟶ a) → Type w

A comonad in a bicategory B is a 1-morphism t : a ⟶ a together with 2-morphisms Δ : t ⟶ t ≫ t and ε : t ⟶ 𝟙 a satisfying the comonad laws.

Defined in
Mathlib.CategoryTheory.Bicategory.Monad.Basic
Cited by
11 results in Mathlib
Foundations
Depth 11 from the axioms · uses propext, Quot.sound
Assumes
CategoryTheory.Bicategory

Around this declaration

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

CategoryTheory.Bicategory.Comonad.comul · cited by 9Comonad.comulCategoryTheory.Bicategory.Comonad.counit · cited by 5Comonad.counitCategoryTheory.Bicategory.OplaxTrans.ComonadBicat.mkOfComonad · cited by 3ComonadBicat.mkOfComonadCategoryTheory.Bicategory.Comonad.comul_assoc · cited by 1Comonad.comul_assocCategoryTheory.Bicategory.Comonad.comul_assoc_flip · cited by 1Comonad.comul_assoc_flipCategoryTheory.Bicategory.Comonad.comul_counit · cited by 1Comonad.comul_counitCategoryTheory.Bicategory.Comonad.counit_comul · cited by 1Comonad.counit_comulCategoryTheory.Bicategory.Comonad.ofOplaxFromUnit · cited by 0Comonad.ofOplaxFromUnitCategoryTheory.Bicategory.Comonad.toOplax · cited by 0Comonad.toOplaxCategoryTheory.Bicategory.Comonad.comul_assoc_assoc · cited by 0Comonad.comul_assoc_assocCategoryTheory.Bicategory.Comonad.comul_assoc_flip_assoc · cited by 0Comonad.comul_assoc_flip_…CategoryTheory.Bicategory.Comonad.comul_counit_assoc · cited by 0Comonad.comul_counit_assocCategoryTheory.Bicategory.Comonad.counit_comul_assoc · cited by 0Comonad.counit_comul_assocCategoryTheory.Bicategory.OplaxTrans.ComonadBicat.mkOfComonad_comul · cited by 0ComonadBicat.mkOfComonad_…CategoryTheory.Bicategory.OplaxTrans.ComonadBicat.mkOfComonad_counit · cited by 0ComonadBicat.mkOfComonad_…Quiver.Hom · cited by 32603Quiver.HomCategoryTheory.Bicategory · cited by 1587CategoryTheory.BicategoryCategoryTheory.ComonObj · cited by 48CategoryTheory.ComonObjBicategory.ComonadCITED BYCITES

Cites3

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

Cited by16

Results whose statement or proof uses this declaration.