Sanjeevi Krishnan

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  Derived Group Completion
  Sanjeevi Krishnan
  Every connected, finite CW complex is homotopy equivalent to the classifying space
  of a monoid [McDuff, 1979], a set with an associative and unital multiplication. Thus group
  completions of monoids correspond to fundamental groups of based spaces. We discuss concrete
  algorithms for computing (co)homology and higher homotopy as algebraic constructions on
  monoids.