Morita cohomology

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.

33 pages

References in corpus (7)

• On (Enriched) Left Bousfield Localization of Model Categories
• Non-finiteness properties of fundamental groups of smooth projective varieties
• Theorie homotopique des DG-categories
• Morita cohomology
• Properness and simplicial resolutions for the model category dgCat
• Morita cohomology and homotopy locally constant sheaves
• Free loop space and homology

Cited by in corpus (10)

• Duality between Lagrangian and Legendrian invariants
• Morita cohomology
• Morita cohomology and homotopy locally constant sheaves
• Homotopy theory of monoids and derived localization
• An ${\mathsf{A}}_{\infty }$ version of the Poincaré lemma
• The global derived period map
• Homological epimorphisms and homotopy epimorphisms
• Singular chains on Lie groups and the Cartan relations II
• Flat Z-graded connections and loop spaces
• The descent of twisted perfect complexes on a space with soft structure sheaf