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Theorems · Definition · commutative algebra

Algebra.TensorProduct.includeLeftRingHom

{R : Type uR} →
  {A : Type uA} →
    {B : Type uB} →
      [inst : CommSemiring R] →
        [inst_1 : Semiring A] →
          [inst_2 : Algebra R A] → [inst_3 : Semiring B] → [inst_4 : Algebra R B] → A →+* TensorProduct R A B

The ring morphism A →+* A ⊗[R] B sending a to a ⊗ₜ 1.

Defined in
Mathlib.RingTheory.TensorProduct.Basic
Cited by
36 results in Mathlib
Foundations
Depth 72 from the axioms · uses propext, Quot.sound
Assumes
CommSemiringSemiringAlgebraSemiringAlgebra

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Algebra.TensorProduct.includeLeft · cited by 72TensorProduct.includeLeftAlgebra.TensorProduct.includeLeftRingHom_apply · cited by 13TensorProduct.includeLeft…CommRingCat.pushoutCocone · cited by 9CommRingCat.pushoutCoconeCommRingCat.isPushout_tensorProduct · cited by 7CommRingCat.isPushout_ten…AlgebraicGeometry.pullbackSpecIso_inv_fst · cited by 7AlgebraicGeometry.pullbac…Algebra.TensorProduct.ringHom_ext · cited by 4TensorProduct.ringHom_extAlgebraicGeometry.pullbackSpecIso_hom_fst · cited by 3AlgebraicGeometry.pullbac…AlgebraicGeometry.mono_pushoutSection_of_iSup_eq · cited by 2AlgebraicGeometry.mono_pu…CommRingCat.epi_iff_epi · cited by 2CommRingCat.epi_iff_epiAlgebra.TensorProduct.map_comp_includeLeftRingHom · cited by 2TensorProduct.map_comp_in…AlgebraicGeometry.of_pullback_fst_Spec_of_codescendsAlong · cited by 2AlgebraicGeometry.of_pull…Algebra.TensorProduct.includeLeftRingHom_comp_algebraMap · cited by 2TensorProduct.includeLeft…CommRingCat.isPushout_of_isPushout · cited by 2CommRingCat.isPushout_of_…AlgebraicGeometry.pullbackSpecIso_hom_fst_assoc · cited by 2AlgebraicGeometry.pullbac…Algebra.IsEffective.eqLocus_includeLeft_includeRight · cited by 1IsEffective.eqLocus_inclu…DFunLike.coe · cited by 62936DFunLike.coeSemiring · cited by 13802SemiringAlgebra · cited by 11388AlgebraCommSemiring · cited by 10911CommSemiringRingHom · cited by 10189RingHomAddMonoidHom · cited by 3230AddMonoidHomTensorProduct · cited by 2545TensorProductLinearMap.flip · cited by 193LinearMap.flipLinearMap.toAddMonoidHom · cited by 101LinearMap.toAddMonoidHomZeroHom.toFun · cited by 101ZeroHom.toFunAddMonoidHom.toZeroHom · cited by 61AddMonoidHom.toZeroHomTensorProduct.AlgebraTensorModule.mk · cited by 10AlgebraTensorModule.mkTensorProduct.includeLeftRing…CITED BYCITES

Cites12

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Cited by38

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