Lemma 76.5.6. Let S be a scheme. Let Z \to Y \to X be immersions of algebraic spaces. Then there is a canonical exact sequence
i^*\mathcal{C}_{Y/X} \to \mathcal{C}_{Z/X} \to \mathcal{C}_{Z/Y} \to 0
where the maps come from Lemma 76.5.3 and i : Z \to Y is the first morphism.
Proof.
Let U be a scheme and let U \to X be a surjective étale morphism. Via Lemmas 76.5.2 and 76.5.4 the exactness of the sequence translates immediately into the exactness of the corresponding sequence for the immersions of schemes Z \times _ X U \to Y \times _ X U \to U. Hence the lemma follows from Morphisms, Lemma 29.31.5.
\square
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