Theorems · Definition · category theory
CategoryTheory.Monad.adj
{C : Type u₁} → [inst : CategoryTheory.Category.{v₁, u₁} C] → (T : CategoryTheory.Monad C) → T.free ⊣ T.forgetThe adjunction between the free and forgetful constructions for Eilenberg-Moore algebras for a monad. cf Lemma 5.2.8 of [Riehl][riehl2017].
- Defined in
- Mathlib.CategoryTheory.Monad.Algebra
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 28 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.
Cites16
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.Functor.objproof · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Functor.mapproof · cited by 8,698
- CategoryTheory.NatTrans.appproof · cited by 7,406
- CategoryTheory.Adjunctionstatement · cited by 524
- CategoryTheory.Monadstatement and proof · cited by 153
- CategoryTheory.Monad.toFunctorproof · cited by 127
- CategoryTheory.Monad.Algebrastatement and proof · cited by 110
- CategoryTheory.Monad.Algebra.Hom.fproof · cited by 48
- CategoryTheory.Monad.Algebra.aproof · cited by 45
Cited by7
Results whose statement or proof uses this declaration.
- CategoryTheory.Adjunction.adjToMonadIsostatement and proof · cited by 2
- CategoryTheory.Monad.adj_counitstatement · cited by 0
- Compactum.adjproof · cited by 0
- CategoryTheory.Under.costarAdjForgetproof · cited by 0
- CategoryTheory.Monad.adj_unitstatement · cited by 0
- CategoryTheory.Adjunction.adjToMonadIso_hom_toNatTrans_appstatement · cited by 0
- CategoryTheory.Adjunction.adjToMonadIso_inv_toNatTrans_appstatement · cited by 0