Not signed in (Sign In)

Start a new discussion

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry beauty bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology combinatorics comma complex-geometry computable-mathematics computer-science constructive constructive-mathematics cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry differential-topology digraphs duality elliptic-cohomology enriched fibration finite foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry graph graphs gravity group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory infinity integration integration-theory k-theory kan lie lie-theory limits linear linear-algebra locale localization logic manifolds mathematics measure-theory modal-logic model model-category-theory monoidal monoidal-category-theory morphism motives motivic-cohomology newpage nonassociative noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pasting philosophy physics planar pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory subobject superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
  1. The book is now out.

    Anonymous

    diff, v5, current

    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeAug 28th 2018

    Forgot to sign in again - that was me.

    Since SDT is an extension of SDG

    By synthetic differential topology (SDT) we shall understand an extension of synthetic differential geometry (SDG) obtained by adding to it axioms of a local nature—to wit, germ representability and the tinyness of the representing objects… which are logical, rather than algebraic infinitesimals. To those, we add four postulates, (excerpt)

    perhaps we might expect the same advantages for a germ-based differential cohesion over SDT, as jet-based differential cohesion over SDG

    A well-known proposal for an axiomatic characterization of infinitesimal objects in a 1-topos goes by the name synthetic differential geometry, where infinitesimal extension is characterized by algebraic properties of dual function algebras, as above. From the point of view and in the presence of cohesion in an ∞-topos, however, there is a more immediate geometric characterization (dcct)

    • CommentRowNumber3.
    • CommentAuthorDavidRoberts
    • CommentTimeAug 28th 2018

    I’m reviewing the book for MathSciNet, it would be good to discuss some of the less familiar concepts and record them on the lab.

    • CommentRowNumber4.
    • CommentAuthorDavid_Corfield
    • CommentTimeAug 28th 2018

    That would be helpful. Is the field sufficiently identified with Bunge that you could record these on synthetic differential topology, or should there be a special page for the book?

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeMar 15th 2019

    added pointer to Penon’s thesis and to logical topology.

    diff, v6, current

Add your comments
  • Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
  • To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

  • (Help)