Cotangent Complex

In mathematics the cotangent complex is a roughly a universal linearization of a morphism of geometric or algebraic objects. Cotangent complexes were originally defined in special cases by a number of authors. Luc Illusie, Daniel Quillen, and M. André independently came up with a definition that works in all cases.

Read more about Cotangent Complex:  Motivation, Early Work On Cotangent Complexes, The Definition of The Cotangent Complex, Examples

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Cotangent Complex - Examples
... Then the cotangent complex is ΩX/S ... We can take the resolution of A to be the identity map, and then it is clear that the cotangent complex is the same as the Kähler differentials ... the exact triangle corresponding to the morphisms X → Y → S, we may determine the cotangent complex LX/Y ...

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