Menu
Home
People
Places
Arts
History
Plants & Animals
Science
Life & Culture
Technology
Reference.org
Bar complex
open-in-new
<p>In mathematics, the bar complex, also called the bar resolution, bar construction, standard resolution, or standard complex, is a way of constructing <a href="/facts/Resolution_(algebra)/xEFm83U7">resolutions</a> in <a href="/facts/Homological_algebra/Jfm8w52l">homological algebra</a>. It was first introduced for the special case of algebras over a <a href="/facts/Commutative_ring/QS1r2ovR">commutative ring</a> by <a href="/facts/Samuel_Eilenberg/vs6aksKX">Samuel Eilenberg</a> and <a href="/facts/Saunders_Mac_Lane/rjgUqfkA">Saunders Mac Lane</a> (1953) and <a href="/facts/Henri_Cartan/IGrXDS4a">Henri Cartan</a> and Eilenberg (1956, IX.6) and has since been generalized in many ways. The name "bar complex" comes from the fact that Eilenberg & Mac Lane (1953) used a vertical bar | as a shortened form of the tensor product ⊗ {\displaystyle \otimes } in their notation for the complex. </p>