Year of Graduation
Applications of the Homotopy Theory of DG Categories
For a topological space X, we define the local systems of complexes - the infinity-category of them and the DG category of them. We conjecture a relation between these two categories. We show that for a path connected space X the complex of chains on based loops is quasiisomorphic to the endomorphism complex of a particular local system and thus it is a DG algebra. We then prove that the DG category of local systems on X is quasiequivalent to the DG category of modules over chains on based loops.