Theorems · Inductive type · category theory
CategoryTheory.Monad.Algebra
{C : Type u₁} → [inst : CategoryTheory.Category.{v₁, u₁} C] → CategoryTheory.Monad C → Type (max u₁ v₁)An Eilenberg-Moore algebra for a monad T.
cf Definition 5.2.3 in [Riehl][riehl2017].
- Defined in
- Mathlib.CategoryTheory.Monad.Algebra
- Cited by
- 110 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 3 definitions · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- CategoryTheory.Monadstatement · cited by 153
Cited by173
Results whose statement or proof uses this declaration.
- CategoryTheory.Monad.Algebra.Astatement and proof · cited by 81
- CategoryTheory.Monad.Algebra.Hom.fstatement and proof · cited by 48
- CategoryTheory.Monad.Algebra.astatement and proof · cited by 45
- CategoryTheory.Monad.forgetstatement and proof · cited by 29
- CategoryTheory.Monad.algebraFunctorOfMonadHomstatement and proof · cited by 15
- CategoryTheory.Monad.freestatement · cited by 15
- CategoryTheory.Monad.comparisonstatement · cited by 14
- CategoryTheory.Monad.Algebra.Homstatement · cited by 11
- Compactumproof · cited by 10
- CategoryTheory.underToAlgebrastatement · cited by 6
- CategoryTheory.algebraToUnderstatement and proof · cited by 5
- CategoryTheory.Monad.algebraFunctorOfMonadHomEqstatement and proof · cited by 5