Definition 76.48.1. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$.

We say $f$ is a

*Koszul morphism*, or that $f$ is a*local complete intersection morphism*if the equivalent conditions of Morphisms of Spaces, Lemma 67.22.1 hold with $\mathcal{P}(f) =$“$f$ is a local complete intersection morphism”.Let $x \in |X|$. We say $f$ is

*Koszul at $x$*if there exists an open neighbourhood $X' \subset X$ of $x$ such that $f|_{X'} : X' \to Y$ is a local complete intersection morphism.

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