Theorems · Definition · category theory
CategoryTheory.Monad.ofMon
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] → CategoryTheory.Mon (CategoryTheory.Functor C C) → CategoryTheory.Monad CTo every monoid object in C ⥤ C we associate a Monad C.
- Defined in
- Mathlib.CategoryTheory.Monad.EquivMon
- Cited by
- 5 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.
Cites8
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.Functorstatement and proof · cited by 16,252
- CategoryTheory.Monstatement and proof · cited by 465
- CategoryTheory.Mon.Xproof · cited by 329
- CategoryTheory.MonObj.mulproof · cited by 230
- CategoryTheory.MonObj.oneproof · cited by 189
- CategoryTheory.Monadstatement · cited by 153
- CategoryTheory.endofunctorMonoidalCategorystatement · cited by 118
Cited by6
Results whose statement or proof uses this declaration.
- CategoryTheory.Monad.monToMonadproof · cited by 7
- CategoryTheory.Monad.ofMon_ηstatement and proof · cited by 0
- CategoryTheory.Monad.ofMon_μstatement and proof · cited by 0
- CategoryTheory.Monad.monToMonad_map_toNatTransstatement · cited by 0
- CategoryTheory.Monad.monToMonad_objstatement · cited by 0
- CategoryTheory.Monad.ofMon_objstatement · cited by 0