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 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 definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration 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 kan lie-theory limit 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 newpage nlab nonassociative noncommutative noncommutative-geometry number-theory object 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).
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeApr 26th 2010
    • (edited Apr 26th 2010)

    ahm, another stupid question: what should sequential colimit point to? directed colimit?

    • CommentRowNumber2.
    • CommentAuthorTodd_Trimble
    • CommentTimeApr 26th 2010

    I think that’s exactly the right place for it. The book on accessible categories by Adamek and Rosicky has some technical details on the relationship between these notions, and that would be good to get recorded here in the Lab. I can do that later when I have some more time.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeApr 26th 2010
    • (edited Apr 26th 2010)

    Thanks, Todd, that would be very helpful. I still don’t have a copy of that book, and reading it in Google-books is a pain. :-/

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeApr 26th 2010

    Eventually it might not be a bad idea for it to be its own page, but directed colimit is also a good redirect.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeApr 26th 2010

    I am actually not sure about the difference. Can you just state it for me?

    • CommentRowNumber6.
    • CommentAuthorMike Shulman
    • CommentTimeApr 26th 2010

    By a sequential colimit I would mean a colimit over an ordinal, or even particularly the ordinal ω\omega, rather than over an arbitrary directed set.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeApr 26th 2010

    Ah, thanks.

    So I created sequential limit now and linked to it from directed limit.

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)