Cotangent complex
In mathematics, the cotangent complex is a common generalisation of the cotangent sheaf, normal bundle and virtual tangent bundle of a map of geometric spaces such as manifolds or schemes. If f : X → Y {\displaystyle f:X\to Y} is a morphism of geometric or algebraic objects, the corresponding cotangent complex L X / Y ∙ {\displaystyle \mathbf {L} _{X/Y}^{\bullet }} can be thought of as a universal "linearization" of it, which serves to control the deformation theory of f {\displaystyle f} .