Theorems · Inductive type · commutative algebra

Algebra.Extension.Hom

{R : Type u} →
  {S : Type v} →
    [inst : CommRing R] →
      [inst_1 : CommRing S] →
        [inst_2 : Algebra R S] →
          Algebra.Extension R S →
            {R' : Type u_1} →
              {S' : Type u_2} →
                [inst_3 : CommRing R'] →
                  [inst_4 : CommRing S'] →
                    [inst_5 : Algebra R' S'] →
                      Algebra.Extension R' S' → [Algebra R R'] → [Algebra S S'] → Type (max u_3 w)

Given a commuting square `` R --→ P -→ S | | ↓ ↓ R' -→ P' → S ` A hom between P and P'` is a ring homomorphism that makes the two squares commute.

Defined in

Mathlib.RingTheory.Extension.Basic

Cited by

51 results in Mathlib

Foundations

Depth 7 from the axioms · uses no axioms

Assumes

CommRingCommRingAlgebraCommRingCommRingAlgebraAlgebraAlgebra