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nLab > Latest Changes: synthetic differential topology

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  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

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