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About: Standard complex     Goto   Sponge   NotDistinct   Permalink

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In mathematics, the standard complex, also called standard resolution, bar resolution, bar complex, bar construction, is a way of constructing resolutions in homological algebra. It was first introduced for the special case of algebras over a commutative ring by Samuel Eilenberg and Saunders Mac Lane and Henri Cartan and Eilenberg and has since been generalized in many ways. The name "bar complex" comes from the fact that used a vertical bar | as a shortened form of the tensor product in their notation for the complex.