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 nonassociative 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

1. • CommentRowNumber1.
   • CommentAuthorporton
   • CommentTimeSep 12th 2013
   • (edited Sep 12th 2013)
   • PermaLink
   Author: porton
   Format: MarkdownItexI have created page <a href="http://nlab.mathforge.org/nlab/show/funcoid">funcoid</a> on nLab wiki. After this I was meet with <a href="http://nforum.mathforge.org/discussion/3911/">some harsh</a>. <blockquote><p>Otherwise, we see you as a stranger writing in our lab book, so to speak, and your stuff will probably just be erased in the end.</p></blockquote> One quote from that conversation: <blockquote><p>Avoiding mention of ϵs and δs is old hat, but cartesian closed categories of spaces are not.</p></blockquote> A few days ago I have proved that my category $\mathbf{Fcd}$ ((proximally) continuous maps between endofuncoids) has all small products and all small co-products. See <a href="http://www.mathematics21.org/binaries/product.pdf">this draft article</a>. Today I've tried to prove that it is cartesian closed (has exponentials) but without much success. By the way, the category $\mathbf{Top}$ can be embedded (in a non-technical sense) into my $\mathbf{Fcd}$ at least in two ways (as Kuratowski closures and as systems of neighborhood filters). This makes my category probably useful for customary general topology (among of properties of $\mathbf{Fcd}$ being interesting by themselves). I ask the nLab authorities to hold back your harsh and allow me to post my stuff into your wiki site. One purpose for this is to distribute my open problem whether $\mathbf{Fcd}$ is cartesian closed ("new hat"). I am not sure whether I am able to solve this myself. Trying together would surely be better. For others to see my research result would also be an advantage. In the meantime, I will probably resign from attempt to investigate whether it is cartesian closed and instead concentrate on researching properties of funcoids similar to compactness of topological spaces. BTW, it is quite likely that $\mathbf{Fcd}$ is even smoother (has more smooth "algebraic properties") than an ordinary cartesian closed category. But the time to investigate this has not yet come. Let lay it as a way for future research in nLab wiki.

   I have created page funcoid on nLab wiki.

   After this I was meet with some harsh.

   Otherwise, we see you as a stranger writing in our lab book, so to speak, and your stuff will probably just be erased in the end.

   One quote from that conversation:

   Avoiding mention of ϵs and δs is old hat, but cartesian closed categories of spaces are not.

   A few days ago I have proved that my category $\mathbf{Fcd}$ ((proximally) continuous maps between endofuncoids) has all small products and all small co-products. See this draft article.

   Today I’ve tried to prove that it is cartesian closed (has exponentials) but without much success.

   By the way, the category $\mathbf{Top}$ can be embedded (in a non-technical sense) into my $\mathbf{Fcd}$ at least in two ways (as Kuratowski closures and as systems of neighborhood filters). This makes my category probably useful for customary general topology (among of properties of $\mathbf{Fcd}$ being interesting by themselves).

   I ask the nLab authorities to hold back your harsh and allow me to post my stuff into your wiki site. One purpose for this is to distribute my open problem whether $\mathbf{Fcd}$ is cartesian closed (“new hat”). I am not sure whether I am able to solve this myself. Trying together would surely be better. For others to see my research result would also be an advantage.

   In the meantime, I will probably resign from attempt to investigate whether it is cartesian closed and instead concentrate on researching properties of funcoids similar to compactness of topological spaces.

   BTW, it is quite likely that $\mathbf{Fcd}$ is even smoother (has more smooth “algebraic properties”) than an ordinary cartesian closed category. But the time to investigate this has not yet come. Let lay it as a way for future research in nLab wiki.

2. • CommentRowNumber2.
   • CommentAuthorMike Shulman
   • CommentTimeSep 12th 2013
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexAs far as I can see, all the objections raised at that discussion still apply.

   As far as I can see, all the objections raised at that discussion still apply.

3. • CommentRowNumber3.
   • CommentAuthorTobyBartels
   • CommentTimeSep 13th 2013
   • PermaLink
   Author: TobyBartels
   Format: MarkdownItexI would particularly suggest following the steps in (2) and (13) (probably in reverse order) from the ‘harsh’ thread.

   I would particularly suggest following the steps in (2) and (13) (probably in reverse order) from the ‘harsh’ thread.

4. • CommentRowNumber4.
   • CommentAuthorTodd_Trimble
   • CommentTimeSep 13th 2013
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexI think #2 from the "harsh" thread is most directly relevant to wanting to write on the nLab. There are occasions where we offer someone a personal web on the nLab complex to record personal research, but that person would have to have established himself or herself first, either via public consensus on strength of publications, or on strength of contributions to the nLab.

   I think #2 from the “harsh” thread is most directly relevant to wanting to write on the nLab. There are occasions where we offer someone a personal web on the nLab complex to record personal research, but that person would have to have established himself or herself first, either via public consensus on strength of publications, or on strength of contributions to the nLab.