Theorems · Theorem · category theory
CategoryTheory.Monad.monToMonad_map_toNatTrans
∀ (C : Type u) [inst : CategoryTheory.Category.{v, u} C] {X Y : CategoryTheory.Mon (CategoryTheory.Functor C C)}
(f : X ⟶ Y), ((CategoryTheory.Monad.monToMonad C).map f).toNatTrans = f.hom- Defined in
- Mathlib.CategoryTheory.Monad.EquivMon
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
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Cites12
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.Homstatement and proof · cited by 32,603
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapstatement and proof · cited by 8,698
- CategoryTheory.Monstatement and proof · cited by 465
- CategoryTheory.Mon.Xstatement · cited by 329
- CategoryTheory.Mon.Hom.homstatement · cited by 200
- CategoryTheory.Monadstatement · cited by 153
- CategoryTheory.endofunctorMonoidalCategorystatement · cited by 118
- CategoryTheory.MonadHom.toNatTransstatement and proof · cited by 21
- CategoryTheory.Monad.monToMonadstatement and proof · cited by 7
- CategoryTheory.Monad.ofMonstatement · cited by 5
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