Theorems · Theorem · category theory
ModuleCat.freeHomEquiv_apply
∀ {R : Type u} [inst : Ring R] {X : Type u} {M : ModuleCat R} (φ : (ModuleCat.free R).obj X ⟶ M),
ModuleCat.freeHomEquiv φ = TypeCat.ofHom fun x => (CategoryTheory.ConcreteCategory.hom φ) (ModuleCat.freeMk x)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
Around this declaration
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- RingHom.idstatement · cited by 18,349
- LinearMapstatement · cited by 10,215
- Equivstatement · cited by 8,337
- Ringstatement and proof · cited by 7,463
- CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
- ModuleCatstatement and proof · cited by 1,429
- ModuleCat.carrierstatement · cited by 997
- TypeCat.ofHomstatement · cited by 389
- ModuleCat.freestatement and proof · cited by 19
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