higher geometry / derived geometry

higher topos theory

higher algebra

geometric little (∞,1)-toposes

structured (∞,1)-topos

geometry (for structured (∞,1)-toposes)

generalized scheme

geometric big (∞,1)-toposes

function algebras on ∞-stacks

loop space object, free loop space object

fundamental ∞-groupoid in a locally ∞-connected (∞,1)-topos / of a locally ∞-connected (∞,1)-topos

derived algebraic geometry

étale (∞,1)-site, Hochschild cohomology of dg-algebras

dg-geometry

schematic homotopy type

derived noncommutative geometry

derived smooth geometry

differential geometry, differential topology

derived smooth manifold, dg-manifold

smooth ∞-groupoid, ∞-Lie algebroid

higher symplectic geometry

higher Klein geometry

higher Cartan geometry

Isbell duality

Jones' theorem, Deligne-Kontsevich conjecture

Tannaka duality for geometric stacks

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