nLab Topos Theoretic Methods in Geometry

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Context

Synthetic differential geometry

synthetic differential geometry

Introductions

from point-set topology to differentiable manifolds

geometry of physics: coordinate systems, smooth spaces, manifolds, smooth homotopy types, supergeometry

Differentials

V-manifolds

smooth space

Tangency

The magic algebraic facts

Theorems

Axiomatics

cohesion

infinitesimal cohesion

tangent cohesion

differential cohesion

graded differential cohesion

singular cohesion

id id fermionic bosonic bosonic Rh rheonomic reduced infinitesimal infinitesimal & étale cohesive ʃ discrete discrete continuous * \array{ && id &\dashv& id \\ && \vee && \vee \\ &\stackrel{fermionic}{}& \rightrightarrows &\dashv& \rightsquigarrow & \stackrel{bosonic}{} \\ && \bot && \bot \\ &\stackrel{bosonic}{} & \rightsquigarrow &\dashv& \mathrm{R}\!\!\mathrm{h} & \stackrel{rheonomic}{} \\ && \vee && \vee \\ &\stackrel{reduced}{} & \Re &\dashv& \Im & \stackrel{infinitesimal}{} \\ && \bot && \bot \\ &\stackrel{infinitesimal}{}& \Im &\dashv& \& & \stackrel{\text{étale}}{} \\ && \vee && \vee \\ &\stackrel{cohesive}{}& \esh &\dashv& \flat & \stackrel{discrete}{} \\ && \bot && \bot \\ &\stackrel{discrete}{}& \flat &\dashv& \sharp & \stackrel{continuous}{} \\ && \vee && \vee \\ && \emptyset &\dashv& \ast }

Models

Lie theory, ∞-Lie theory

differential equations, variational calculus

Chern-Weil theory, ∞-Chern-Weil theory

Cartan geometry (super, higher)

This page is to record the reference:

  • Anders Kock (ed.):


    Topos Theoretic Methods in Geometry


    Various Publications Series 30

    Aarhus University (1979)

    pdf, pdf

compiling early discussions of synthetic differential geometry.

Contents:

  • F. William Lawvere:

    Categorical dynamics

  • Marie-Françoise Coste, Michel Coste:

    The generic model of an ϵ\epsilon-stable geometric extension of the theory of rings is of line type

  • Marie-Françoise Coste, Michel Coste:

    Topologies for real algebraic geometry

  • E. J. Dubuc, G. E. Reyes:

    Subtoposes of the ring classifier

  • Anders Kock:

    Formally real local rings, and infinitesimal stability

  • Peter T. Johnstone:

    Extracts from two letters to Anders Kock, March 1978

  • Anders Kock:

    On the synthetic theory of vector fields

  • A. Kock, G. E. Reyes:

    Connections in formal differential geometry

  • Christiane Rousseau:

    Complex structures on topoi

  • G. C. Wraith:

    Complexification of variable fields

  • Report on the Open House on Topos Theoretic Methods in Geometry and Analysis, Aarhus, May 10–24, 1978.

category: reference

Last revised on December 22, 2025 at 15:06:59. See the history of this page for a list of all contributions to it.