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Theorems · Theorem · category theory

ModuleCat.monoidAlgebraFree_map

∀ (R : Type u) [inst : Ring R] {X Y : Type u} (f : X ⟶ Y),
  (ModuleCat.monoidAlgebraFree R).map f =
    ModuleCat.ofHom (MonoidAlgebra.mapDomainLinearMap R R ⇑(CategoryTheory.ConcreteCategory.hom f))
Defined in
Mathlib.Algebra.Category.ModuleCat.Adjunctions
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Foundations
Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Ring
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DFunLike.coe · cited by 62936DFunLike.coeQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.map · cited by 8698Functor.mapRing · cited by 7463RingCategoryTheory.ConcreteCategory.hom · cited by 4022ConcreteCategory.homModuleCat · cited by 1429ModuleCatTypeCat.Fun · cited by 1307TypeCat.FunModuleCat.of · cited by 594ModuleCat.ofMonoidAlgebra · cited by 590MonoidAlgebraModuleCat.ofHom · cited by 200ModuleCat.ofHomMonoidAlgebra.mapDomainLinearMap · cited by 17MonoidAlgebra.mapDomainLi…ModuleCat.monoidAlgebraFree · cited by 3ModuleCat.monoidAlgebraFr…ModuleCat.monoidAlgebraFree_m…CITED BYCITES

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