Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

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 definitions 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 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 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 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

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeApr 26th 2010
   • (edited Apr 26th 2010)
   • PermaLink
   Author: Urs
   Format: MarkdownItexahm, another stupid question: what should [[sequential colimit]] point to? [[directed colimit]]?

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

2. • CommentRowNumber2.
   • CommentAuthorTodd_Trimble
   • CommentTimeApr 26th 2010
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexI 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.

   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.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeApr 26th 2010
   • (edited Apr 26th 2010)
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks, 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. :-/

   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. :-/

4. • CommentRowNumber4.
   • CommentAuthorMike Shulman
   • CommentTimeApr 26th 2010
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexEventually it might not be a bad idea for it to be its own page, but [[directed colimit]] is also a good redirect.

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

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeApr 26th 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItexI am actually not sure about the difference. Can you just state it for me?

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

6. • CommentRowNumber6.
   • CommentAuthorMike Shulman
   • CommentTimeApr 26th 2010
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexBy a sequential colimit I would mean a colimit over an ordinal, or even particularly the ordinal $\omega$, rather than over an arbitrary directed set.

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

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeApr 26th 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItexAh, thanks. So I created [[sequential limit]] now and linked to it from [[directed limit]].

   Ah, thanks.

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