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Is there a cotangent bundle of a stable $\infty$-category?

In the years since this question was asked, some of the theory the OP wanted was developed. First, in Lurie's Higher Algebra, Definition defines the absolute cotangent complex functor $L: C\...
David White's user avatar
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6 votes

Exact sequences in Positselski's coderived category induce distinguished triangles

Yes, of course. The coderived and contraderived categories (or more specifically, the absolute derived categories) are defined precisely in such a way that short exact sequences of CDG-modules induce ...
Leonid Positselski's user avatar

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