Justin R. Smith

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This paper constructs model structures on the categories of coalgebras and pointed irreducible coalgebras over an operad whose components are projective, finitely generated in each dimension, and satisfy a condition that allows one to take tensor products with a unit interval. The underlying chain-complex is assumed to be unbounded and the results for(More)
This paper explicitly constructs cofree coalgebras over operads in the category of DG-modules. It is shown that the existence of an operad-action on a coalgebra implies a " generalized coassociativity " that facilitates the construction. Special cases are considered in which the general expression simplifies (such as the pointed, irreducible case). In the(More)
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(More)
This paper constructs model structures on the categories of coalgebras and pointed irreducible coalgebras over an operad whose components are projective, finitely generated in each dimension, and satisfy a condition that allows one to take tensor products with a unit interval. The underlying chain-complex is assumed to be unbounded and the results for(More)
Uterine transplantation has been proposed as a possible solution to absolute uterine factor infertility untreatable by any other option. Since the first human attempt in 2000, various teams have tried to clarify which immunosuppressant would be most suitable for protecting the allogeneic uterine graft while posing a minimal risk to the fetus. Cyclosporine A(More)
a r t i c l e i n f o a b s t r a c t This paper shows that a functorial version of the " higher diagonal " of a space used to compute Steenrod squares actually contains far more topological information — including (in some cases) the space's integral homotopy type.