Morita cohomology

Holstein, Julian V. S. (2015) Morita cohomology. Mathematical Proceedings of the Cambridge Philosophical Society, 158 (1). pp. 1-26. ISSN 0305-0041

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Abstract

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.