Theorems · Definition · commutative algebra

AlgHom.pullback

{R : Type u_1} →
  {A : Type u_2} →
    {B : Type u_3} →
      {C : Type u_4} →
        [inst : CommSemiring R] →
          [inst_1 : Semiring A] →
            [inst_2 : Algebra R A] →
              [inst_3 : Semiring B] →
                [inst_4 : Algebra R B] →
                  [inst_5 : Semiring C] → [inst_6 : Algebra R C] → (A →ₐ[R] C) → (B →ₐ[R] C) → Subalgebra R (A × B)

The subalgebra of pairs (a, b) : A × B such that f a = g b, i.e., the pullback of f and g as a subalgebra of A × B.

Defined in

Mathlib.RingTheory.LocalRing.Pullback

Cited by

5 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringAlgebraSemiringAlgebraSemiringAlgebra