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higher geometry - contents

higher geometry

Ingredients

• higher topos theory

• higher algebra

Concepts

• notions of space

• (∞,1)-topos

  • ∞-space

  • ∞-stack

  • derived stack

  • internal ∞-groupoid

    • topological ∞-groupoid

    • ∞-Lie groupoid

• structured (∞,1)-topos

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

  • generalized scheme

Examples

• derived algebraic geometry

  • simplicial ring

  • E-∞ ring

• derived noncommutative geometry

  • noncommutative geometry

  • A-∞-category

• derived smooth geometry

  • C∞-ring/smooth locus

  • derived smooth manifold

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