Morita cohomology
  We consider two categorifications of the cohomology of a topological space X by taking coefficients in the category of differential graded categories. We consider both derived global sections of a constant presheaf and singular cohomology and find the resulting dg-categories are quasi-equivalent and moreover quasi-equivalent to representations in perfect complexes of chains on the loop space of X. 
Julian V. S. Holstein
math.AT math.CT