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Let $R$ be an (animated) commutative ring, with cotangent complex $L_R$ and let $\mathcal{C}(R) = \mathcal{D}(R)_{\Sigma^{-1}L_R/}$ be the category of nice square zero extensions of $R$. A typical ...

I'm trying to understand cotangent complexes and their role in deformation theory, and later the statement that they're somehow natural in a derived scheme/stack. I understand that the standard ...