It seems to me that a lot of people do deformation theory (of schemes, sheaves, maps etc) in derived category (of an appropriate abelian category). For example, the cotangent complex of a morphism ...
I have several naive and possibly stupid questions about deformations of categories. I hope that someone can at least point me to some appropriate references. What is a deformation of a (linear, dg, ...
Does anyone have an answer to the question "What does the cotangent complex measure?" Algebraic intuitions (like "homology measures how far a sequence is from being exact") are as welcome as ...