Theorems · Theorem · category theory
CategoryTheory.Comonad.algebra_mono_of_mono
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] (G : CategoryTheory.Comonad C) {X Y : G.Coalgebra}
(f : X ⟶ Y) [h : CategoryTheory.Mono f.f], CategoryTheory.Mono fGiven a coalgebra morphism whose carrier part is a monomorphism, we get an algebra monomorphism.
- Defined in
- Mathlib.CategoryTheory.Monad.Algebra
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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.Monostatement and proof · cited by 893
- CategoryTheory.Comonadstatement and proof · cited by 125
- CategoryTheory.Comonad.Coalgebrastatement and proof · cited by 114
- CategoryTheory.Comonad.Coalgebra.Astatement · cited by 75
- CategoryTheory.Comonad.Coalgebra.Hom.fstatement and proof · cited by 46
- CategoryTheory.Comonad.forgetproof · cited by 29
- CategoryTheory.Functor.mono_of_mono_mapproof · cited by 24
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.