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-categories 2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex-geometry computable-mathematics computer-science constructive cosmology 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 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 limit limits linear linear-algebra locale localization logic manifolds mathematics measure-theory modal modal-logic model model-category-theory monads monoidal monoidal-category-theory morphism motives motivic-cohomology natural 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 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).

nLab > Latest Changes: finite set

Bottom of Page

1 to 7 of 7

  1.  
    • CommentRowNumber1.
    • CommentAuthorDavid_Corfield
    • CommentTimeJan 27th 2021

    Added

    For a treatment in homotopy type theory see

    • Dan Frumin, Herman Geuvers, Léon Gondelman, Niels van der Weide, Finite Sets in Homotopy Type Theory, (pdf)

    diff, v46, current

  2. Re-organised slightly. Added a brief introductory section, moved a couple of paragraphs of existing content into it. Removed the two context menus ’foundations’ and ’mathematics’ which I don’t think really fit here (the latter is arguably too general to be useful on any page).

    Intend to add a new section in a subsequent edit.

    diff, v47, current

  3. Added a section explaining how to view a finite set as a scheme (over any base).

    diff, v48, current

    • CommentRowNumber4.
    • CommentAuthorUlrik
    • CommentTimeFeb 22nd 2021

    Richard, maybe we can mention (in the “Viewing as schemes” section) that a finite coproduct of affine schemes SpecR iSpec R_i, i=1,…,ni=1,\ldots,n, is again affine, Spec(R 1×⋯×R n)Spec (R_1 \times \cdots \times R_n). Taking R i=ℤR_i=\mathbb{Z}, we can view the finite set XX as the (affine) scheme Spec(ℤ X)Spec (\mathbb{Z}^X). This agrees with what you wrote, but seems more canonical.

    • CommentRowNumber5.
    • CommentAuthorRichard Williamson
    • CommentTimeFeb 22nd 2021
    • (edited Feb 22nd 2021)

    Nice! Great if you can go ahead and make an edit if you have time, as I’ll be tied up until the evening European time!

    Maybe keep the explicit description, but add the nice canonical one in addition?

    • CommentRowNumber6.
    • CommentAuthorUlrik
    • CommentTime7 days ago

    Alternative description of finite sets as affine schemes.

    diff, v51, current

  7. Thanks for the edit!

1 to 7 of 7

  1.  
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)
 
Back to Discussions Top of Page