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 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 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 internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure 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).

nLab > Latest Changes: Isbell duality - table

Bottom of Page

1 to 9 of 9

  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJul 23rd 2018

    the table didn’t have the basic examples, such as Gelfand duality and Milnor’s exercise. Added now.

    diff, v4, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJul 26th 2018

    added one more line to the table (super L ∞L_\infty-algebras ↔\leftrightarrow differential graded-commutative superalgebras)

    diff, v5, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJul 26th 2018
    • (edited Jul 26th 2018)

    added pointer to the equivalence between fully faithfulness of affine schemes in opposites of rings.

    Undecided now whether to display mostly full inclusions or the equivalences onto their essential image. Table may deserve further reworking..

    diff, v6, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJan 22nd 2021
    • (edited Jan 22nd 2021)

    In revision 12 from October 2020, an anonymous edit tried to hyperlink the words “Gelfand-Kolmogorov”, but failed. I have fixed this now.

    Of course the issue is that the hyperlinks are inside a \text-environment inside a maths environment, and so necessarlily (?) Instiki syntax doesn’t work here – but HTML still does…

    … or at least it does with Firefox. I suppose most other browsers show just broken links on this page here?

    diff, v13, current

    • CommentRowNumber5.
    • CommentAuthorDavid_Corfield
    • CommentTimeJan 22nd 2021

    I’m just seeing “Unknown node type: a” in Chrome.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeOct 19th 2021
    • (edited Oct 19th 2021)

    I have changed the table header from “Isbell duality” to “duality between algebra and geometry”. The former was meant to be read as a synonym for the latter, but I can see how that’s too ideosyncratic not to be confusing (as per the discussion here).

    For the moment the page title (which is not displayed in the pages where this table is !include-ed) remains the same. Because I am unsure if the software would correctly handle !redirects inside !includes, and since I don’t have the time now to search for and change all the !include-commands to this table.

    diff, v14, current

    • CommentRowNumber7.
    • CommentAuthorzskoda
    • CommentTimeSep 12th 2024
    • (edited Sep 12th 2024)

    The table lists affine schemes as a (edit:) subcategory of finitely generated commutative algebras.

    The category of affine schemes is antiequivalent to the category of all commutative rings. One can work over some ground ring kk if wanted, but finite generation is not needed for anything unless it is required at both sides. Some people consider just “affine algebras” over some kk, but usually when talking the case of varieties.

    However, spectrum can also be understood as a right adjoint to the global sections functor on the category of locally affine ringed spaces.

    I do not know what the author meant with putting these finiteness requirements in the table.

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeSep 12th 2024

    Hm, I forget why I put in that qualifiers. Let’s remove it.

    • CommentRowNumber9.
    • CommentAuthorzskoda
    • CommentTimeSep 12th 2024

    Done.

1 to 9 of 9

  1.