Theorems · Definition · category theory
CategoryTheory.Monad.monToMonad
(C : Type u) →
[inst : CategoryTheory.Category.{v, u} C] →
CategoryTheory.Functor (CategoryTheory.Mon (CategoryTheory.Functor C C)) (CategoryTheory.Monad C)Passing from Mon (C ⥤ C) to Monad C is functorial.
- Defined in
- Mathlib.CategoryTheory.Monad.EquivMon
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 35 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.
Cites9
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.Homproof · cited by 32,603
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Monstatement and proof · cited by 465
- CategoryTheory.Mon.Xproof · cited by 329
- CategoryTheory.Mon.Hom.homproof · cited by 200
- CategoryTheory.Monadstatement · cited by 153
- CategoryTheory.endofunctorMonoidalCategorystatement · cited by 118
- CategoryTheory.Monad.ofMonproof · cited by 5
Cited by8
Results whose statement or proof uses this declaration.
- CategoryTheory.Monad.monadMonEquivproof · cited by 6
- CategoryTheory.Monad.monadMonEquiv_unitIso_hom_app_toNatTrans_appstatement · cited by 0
- CategoryTheory.Monad.monadMonEquiv_unitIso_inv_app_toNatTrans_appstatement · cited by 0
- CategoryTheory.Monad.monToMonad_map_toNatTransstatement and proof · cited by 0
- CategoryTheory.Monad.monToMonad_objstatement and proof · cited by 0
- CategoryTheory.Monad.monadMonEquiv_counitIso_hom_app_homstatement · cited by 0
- CategoryTheory.Monad.monadMonEquiv_counitIso_inv_app_homstatement · cited by 0
- CategoryTheory.Monad.monadMonEquiv_inversestatement · cited by 0