Theorems · Theorem · commutative algebra

Algebra.Extension.tensorCotangent.congr_simp

∀ {R : Type u_1} {S : Type u_2} {T : Type u_3} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : CommRing T]
  [inst_3 : Algebra R S] [inst_4 : Algebra R T] [inst_5 : Algebra S T] {P : Algebra.Extension R S}
  {Q : Algebra.Extension R T} (f f_1 : P.Hom Q) (e_f : f = f_1) [alg : Algebra P.Ring Q.Ring]
  (halg : algebraMap P.Ring Q.Ring = f.toRingHom)
  (H : Function.Bijective ⇑(LinearMap.liftBaseChange Q.Ring (f.mapKer halg))),
  Algebra.Extension.tensorCotangent f halg H = Algebra.Extension.tensorCotangent f_1 ⋯ ⋯

Defined in

Mathlib.RingTheory.Etale.Kaehler

Cited by

0 results in Mathlib

Foundations

Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingCommRingAlgebraAlgebraAlgebraAlgebra