Theorems · Definition · commutative algebra
PolynomialLaw.toFun
{R : Type u} →
[inst : CommSemiring R] →
{M : Type u_1} →
[inst_1 : AddCommMonoid M] →
[inst_2 : Module R M] →
{N : Type u_2} →
[inst_3 : AddCommMonoid N] →
[inst_4 : Module R N] →
(S : Type v) →
[inst_5 : CommSemiring S] →
[inst_6 : Algebra R S] → (M →ₚₗ[R] N) → TensorProduct R S M → TensorProduct R S NThe extension of PolynomialLaw.toFun' to all universes.
- Defined in
- Mathlib.RingTheory.PolynomialLaw.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- AddCommMonoidstatement and proof · cited by 12,281
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- TensorProductstatement and proof · cited by 2,545
- Function.extendproof · cited by 111
- PolynomialLawstatement and proof · cited by 37
- PolynomialLaw.πproof · cited by 11
- PolynomialLaw.toFunLiftedproof · cited by 2
Cited by12
Results whose statement or proof uses this declaration.
- PolynomialLaw.toFun_eq_rTensor_φ_toFun'statement · cited by 7
- PolynomialLaw.isCompat_applystatement and proof · cited by 2
- PolynomialLaw.toFun'_eq_toFunstatement · cited by 1
- PolynomialLaw.toFun_add_applystatement · cited by 1
- PolynomialLaw.toFun_compstatement and proof · cited by 1
- PolynomialLaw.toFun_addstatement and proof · cited by 0
- PolynomialLaw.toFun_comp_applystatement and proof · cited by 0
- PolynomialLaw.toFun_negstatement · cited by 0
- PolynomialLaw.isCompatstatement and proof · cited by 0
- PolynomialLaw.toFun_smulstatement · cited by 0
- PolynomialLaw.toFun_zerostatement · cited by 0
- PolynomialLaw.one_tmul_groundstatement and proof · cited by 0