High Quality Content by WIKIPEDIA articles! 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. Andre independently came up with a definition that works in all cases.Suppose that X and Y are algebraic varieties and that f : X -> Y is a morphism between them. The cotangent complex of f is a more universal version of the relative Kahler differentials X/Y. The most basic motivation for such an object is the exact sequence of Kahler differentials associated to two morphisms.

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