Theorems · Theorem · ring theory
MatrixModCat.isScalarTower_toModuleCat
∀ (R : Type u) {ι : Type v} [inst : Ring R] [inst_1 : Fintype ι] [inst_2 : DecidableEq ι]
(M : ModuleCat (Matrix ι ι R)), IsScalarTower R (Matrix ι ι R) ↑M- Defined in
- Mathlib.RingTheory.Morita.Matrix
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingFintypeDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Fintypestatement and proof · cited by 7,736
- Ringstatement and proof · cited by 7,463
- Matrixstatement and proof · cited by 4,303
- IsScalarTowerstatement · cited by 3,896
- ModuleCatstatement and proof · cited by 1,429
- ModuleCat.carrierstatement and proof · cited by 997
- Matrix.diagonalproof · cited by 314
- SemigroupAction.mul_smulproof · cited by 291
- Matrix.scalarstatement and proof · cited by 62
- Module.compHomstatement · cited by 39
- Matrix.smul_eq_diagonal_mulproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- toModuleCatFromModuleCatLinearEquivstatement · cited by 0
- MatrixModCat.toModuleCat_mapstatement · cited by 0
- MatrixModCat.toModuleCat_obj_carrierstatement · cited by 0