nLab
synthetic differential geometry - contents

synthetic differential geometry

Axiomatics

• lined topos

  • interval object

• smooth topos

  • infinitesimal space

    • amazing right adjoint

    • infinitesimal interval object

  • Kock-Lawvere axiom

  • integration axiom

• super smooth topos

• infinitesimal path ∞-groupoid

  • microlinear space

  • tangent bundle

  • differential forms

• smooth path ∞-groupoid

Models

• Models for Smooth Infinitesimal Analysis

  • Fermat theory

  • smooth algebra (C-∞-ring)

  • smooth loci

  • smooth natural numbers

Variations

• synthetic differential supergeometry

• smooth (∞,1)-topos

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