M-structures Determine Integral Homotopy Type

  title={M-structures Determine Integral Homotopy Type},
  author={Justin R. Smith},
This paper proves that the functor C(∗) that sends pointed, simply-connected CW-complexes to their chain-complexes equipped with diagonals and iterated higher diagonals, determines their integral homotopy type — even inducing an equivalence of categories between the category of CW-complexes up to homotopy equivalence and a certain category of chain-complexes equipped with higher diagonals. Consequently, C(∗) is an algebraic model for integral homotopy types similar to Quillen’s model of… CONTINUE READING