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 BThe 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
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- AddMonoidHomproof · cited by 3,230
- TensorProductstatement and proof · cited by 2,545
- LinearMap.flipproof · cited by 193
- LinearMap.toAddMonoidHomproof · cited by 101
- ZeroHom.toFunproof · cited by 101
- AddMonoidHom.toZeroHomproof · cited by 61
- TensorProduct.AlgebraTensorModule.mkproof · cited by 10
Cited by38
Results whose statement or proof uses this declaration.
- Algebra.TensorProduct.includeLeftproof · cited by 72
- Algebra.TensorProduct.includeLeftRingHom_applystatement and proof · cited by 13
- CommRingCat.pushoutCoconeproof · cited by 9
- CommRingCat.isPushout_tensorProductstatement and proof · cited by 7
- AlgebraicGeometry.pullbackSpecIso_inv_fststatement · cited by 7
- Algebra.TensorProduct.ringHom_extstatement and proof · cited by 4
- AlgebraicGeometry.pullbackSpecIso_hom_fststatement · cited by 3
- AlgebraicGeometry.mono_pushoutSection_of_iSup_eqproof · cited by 2
- CommRingCat.epi_iff_epiproof · cited by 2
- Algebra.TensorProduct.map_comp_includeLeftRingHomstatement · cited by 2
- AlgebraicGeometry.of_pullback_fst_Spec_of_codescendsAlongproof · cited by 2
- Algebra.TensorProduct.includeLeftRingHom_comp_algebraMapstatement · cited by 2