Lemma 37.62.5. Let $f : X = \mathop{\mathrm{Spec}}(B) \to S = \mathop{\mathrm{Spec}}(A)$ be a morphism of affine schemes. Then $f$ is a local complete intersection morphism if and only if $A \to B$ is a local complete intersection homomorphism, see More on Algebra, Definition 15.33.2.

**Proof.**
Follows immediately from the definitions.
$\square$

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