Theorems · Definition · category theory
CategoryTheory.Monad.monadMonEquiv
(C : Type u) →
[inst : CategoryTheory.Category.{v, u} C] → CategoryTheory.Monad C ≌ CategoryTheory.Mon (CategoryTheory.Functor C C)Oh, monads are just monoids in the category of endofunctors (equivalence of categories).
- Defined in
- Mathlib.CategoryTheory.Monad.EquivMon
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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.Functor.objproof · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.compproof · cited by 6,529
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- CategoryTheory.Functor.idproof · cited by 3,333
- CategoryTheory.Equivalencestatement · cited by 601
- CategoryTheory.Monstatement and proof · cited by 465
- CategoryTheory.Mon.Xproof · cited by 329
- CategoryTheory.Monadstatement and proof · cited by 153
- CategoryTheory.Monad.toFunctorproof · cited by 127
- CategoryTheory.endofunctorMonoidalCategorystatement · cited by 118
Cited by6
Results whose statement or proof uses this declaration.
- CategoryTheory.Monad.monadMonEquiv_unitIso_hom_app_toNatTrans_appstatement and proof · cited by 0
- CategoryTheory.Monad.monadMonEquiv_unitIso_inv_app_toNatTrans_appstatement and proof · cited by 0
- CategoryTheory.Monad.monadMonEquiv_counitIso_hom_app_homstatement and proof · cited by 0
- CategoryTheory.Monad.monadMonEquiv_counitIso_inv_app_homstatement and proof · cited by 0
- CategoryTheory.Monad.monadMonEquiv_functorstatement and proof · cited by 0
- CategoryTheory.Monad.monadMonEquiv_inversestatement and proof · cited by 0