Theorems · Theorem · commutative algebra
Algebra.TensorProduct.ringHom_ext
∀ {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] {C : Type u_3} [inst_5 : Semiring C] {f g : TensorProduct R A B →+* C},
f.comp Algebra.TensorProduct.includeLeftRingHom = g.comp Algebra.TensorProduct.includeLeftRingHom →
f.comp Algebra.TensorProduct.includeRight.toRingHom = g.comp Algebra.TensorProduct.includeRight.toRingHom → f = g- Defined in
- Mathlib.RingTheory.TensorProduct.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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 and proof · cited by 10,189
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- TensorProductstatement and proof · cited by 2,545
- map_zeroproof · cited by 1,614
- TensorProduct.tmulproof · cited by 1,182
- map_addproof · cited by 964
- RingHom.compstatement and proof · cited by 899
Cited by4
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.mono_pushoutSection_of_iSup_eqproof · cited by 2
- Ideal.Fiber.lift_residueField_surjectiveproof · cited by 1
- Algebra.TensorProduct.ringHom_ext_iffproof · cited by 0