Lemma 76.44.9. Let S be a scheme. Let i : Z \to Y and j : Y \to X be immersions of algebraic spaces over S. Assume that the sequence
0 \to i^*\mathcal{C}_{Y/X} \to \mathcal{C}_{Z/X} \to \mathcal{C}_{Z/Y} \to 0
of Lemma 76.5.6 is exact and locally split.
If j \circ i is a quasi-regular immersion, so is i.
If j \circ i is a H_1-regular immersion, so is i.
If both j and j \circ i are Koszul-regular immersions, so is i.
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