We introduce the notions of infinitesimal extension and square-zero extension in the context of simplicial commutatie algebras. We next investigate their mutual relationship and we show that the Postnikov tower of a simplicial commutative algebra is built out of square-zero extensions. We conclude the notes with two applications: we give connectivity estimates for the cotangent complex and we show how obstructions can be seen as deformations over simplicial rings.
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