Theorems · Theorem · linear algebra
Submodule.mulMap_map_comp_eq
∀ {R : Type u} {S : Type v} [inst : CommSemiring R] [inst_1 : Semiring S] [inst_2 : Algebra R S] (M N : Submodule R S)
{T : Type w} [inst_3 : Semiring T] [inst_4 : Algebra R T] (f : S →ₐ[R] T),
(Submodule.map (↑f) M).mulMap (Submodule.map (↑f) N) ∘ₗ
TensorProduct.map ((↑f).submoduleMap M) ((↑f).submoduleMap N) =
↑f ∘ₗ M.mulMap N- Cited by
- 1 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Submodulestatement and proof · cited by 7,192
- AlgHomstatement and proof · cited by 3,236
- TensorProductstatement · cited by 2,545
- LinearMap.compstatement and proof · cited by 1,642
- map_mulproof · cited by 1,137
- LinearMap.extproof · cited by 844
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.coe_mulMap_comp_eqproof · cited by 1