Not signed in (Sign In)

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 book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics comma complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group 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 integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics 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 superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft 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).
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeOct 4th 2009

    I worked on synthetic differential geometry:

    I rearranged slightly and then expanded the "Idea" section, trying to give a more comprehensive discussion and more links to related entries. Also added more (and briefly commented) references. Much more about references can probably be said, I have only a vague idea of the "prehistory" of the subject, before it became enshrined in the textbooks by Kock, Lavendhomme and Moerdijk-Reyes.

    Also, does anyone have an electronic copy of that famous 1967 lecture by Lawvere on "categorical dynamics"? It would be nice to have an entry on that, as it seems to be a most visionary and influential text. If I understand right it gave birth to topos theory, to synthetic differential geometry and all that just as a spin-off of a more ambitious program to formalize physics. If I am not mistaken, we are currently at a point where finally also that last bit is finding a full implmenetation as a research program.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeOct 31st 2020

    added DOI-s to:

    diff, v74, current

    • CommentRowNumber3.
    • CommentAuthorGuest
    • CommentTimeOct 9th 2021

    Re remark 2.1 (Peirce’s quote that the “idea of an infinitesimal involves no contradiciton” supposedly foreshadowing non-classical logic): doesn’t he rather mean that the concept of infinitesimal is not inconsistent? The immediately preceding paragraph in the article (Peirce 1892: 537) is this (emphasis mine):

    Most of the mathematicians who during the last two generations have treated the differential calculus have been of the opinion that an infinitesimal quantity is an absurdity ; although, with their habitual caution, they have often added “or, at any rate, the conception of an infinitesimal is so difficult, that we practically cannot reason about it with confidence and security.” Accordingly, the doctrine of limits has been invented to evade the difficulty, or, as some say, to explain the signification of the word “infinitesimal.” This doctrine, in one form or another, is taught in all the text-books, though in some of them only as an alternative view of the matter ; it answers well enough the purposes of calculation, though even in that application it has its difficulties.

    • CommentRowNumber4.
    • CommentAuthorThomas Holder
    • CommentTimeOct 9th 2021

    Sorry for being unclear: the Peirce quote is intended to exhibit only his advocacy of infinitesimals. I added a further quote (from John Bell) as a pointer to his views of the role of LEM in “this” context. In fact, the passage on LEM that Bell goes on quoting concerns points on a continuous line for which LEM is supposed to be invalid and is taken from a 1903 note of Peirce published in vol.III of “The New Elements of Mathematics”, p.xvi. Feel free to improve the passage!

    diff, v76, current

    • CommentRowNumber5.
    • CommentAuthorGuest
    • CommentTimeApr 21st 2022

    Wikipedia has this article called Abstract differential geometry

  1. Added reference

    Anonymous

    diff, v77, current

  2. correcting typo “syntehtic algebraic geometry” -> “synthetic algebraic geometry”

    Theresa

    diff, v83, current