Theorems · Definition · category theory
CategoryTheory.Adjunction.adjToMonadIso
{C : Type u₁} → [inst : CategoryTheory.Category.{v₁, u₁} C] → (T : CategoryTheory.Monad C) → T.adj.toMonad ≅ TThe monad induced by the Eilenberg-Moore adjunction is the original monad.
- Defined in
- Mathlib.CategoryTheory.Monad.Adjunction
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 31 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.
Cites13
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.Isostatement · cited by 3,963
- CategoryTheory.Iso.reflproof · cited by 727
- CategoryTheory.NatIso.ofComponentsproof · cited by 178
- CategoryTheory.Monadstatement and proof · cited by 153
- CategoryTheory.Monad.toFunctorproof · cited by 127
- CategoryTheory.Monad.Algebrastatement · cited by 110
- CategoryTheory.Monad.forgetstatement · cited by 29
- CategoryTheory.Adjunction.toMonadstatement and proof · cited by 22
- CategoryTheory.Monad.freestatement · cited by 15
- CategoryTheory.Monad.adjstatement and proof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.Adjunction.adjToMonadIso_hom_toNatTrans_appstatement and proof · cited by 0
- CategoryTheory.Adjunction.adjToMonadIso_inv_toNatTrans_appstatement and proof · cited by 0