# nLab geometry

geometry $\leftarrow$ Isbell duality $\rightarrow$ algebra

## Theorems

and pages on various cohomologies, including sheaf cohomology, nonabelian cohomology, differential cohomology, Deligne cohomology, etale cohomology, equivariant cohomology, Bredon cohomology and their cocycle classes including torsors, gerbes, principal 2-bundles as well as the related picture of the descent theory (cf. oriental, descent for simplicial presheaves…). A modern systematic theory of cohomology and descent can be done using the language of $(\infinity,1)$-categories and abstract homotopy theory, say via Quillen model categories (e.g. of simplicial presheaves).