Theorems · Definition · category theory
SemimoduleCat.of
(R : Type u) → [inst : Semiring R] → (X : Type v) → [inst_1 : AddCommMonoid X] → [Module R X] → SemimoduleCat R
The object in the category of R-algebras associated to a type equipped with the appropriate
typeclasses. This is the preferred way to construct a term of SemimoduleCat R.
- Defined in
- Mathlib.Algebra.Category.ModuleCat.Semi
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- SemimoduleCatstatement · cited by 108
Cited by36
Results whose statement or proof uses this declaration.
- CommRing.Pic.mkproof · cited by 17
- SemimoduleCat.ofHomstatement · cited by 12
- SemimoduleCat.MonoidalCategory.tensorObjproof · cited by 12
- LinearEquiv.toModuleIsoₛstatement · cited by 7
- CommRing.Pic.mk.linearEquivproof · cited by 3
- SemimoduleCat.Hom.hom₂statement and proof · cited by 3
- SemimoduleCat.ofHom₂statement · cited by 3
- SemimoduleCat.MonoidalCategory.leftUnitorstatement · cited by 3
- SemimoduleCat.MonoidalCategory.rightUnitorstatement · cited by 3
- LinearEquiv.toModuleIsoₛ_homstatement · cited by 2
- CommRing.Pic.mk_tensorproof · cited by 2
- linearEquivIsoModuleIsoₛstatement and proof · cited by 2