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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 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 nforum 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 sheaves 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.
   • CommentAuthorPeter Heinig
   • CommentTimeJun 5th 2017
   • (edited Jun 5th 2017)
   • PermaLink
   Author: Peter Heinig
   Format: MarkdownItexCreated [[SomePage > naturalitysquare20170605]], following some instruction in the HowTo pages. Diagram is planned to be used in the next few days in analytical part of the unfinished article [[unnatural isomorphism]], the writing of which had to be broken off.

   Created SomePage > naturalitysquare20170605, following some instruction in the HowTo pages. Diagram is planned to be used in the next few days in analytical part of the unfinished article unnatural isomorphism, the writing of which had to be broken off.

2. • CommentRowNumber2.
   • CommentAuthorTodd_Trimble
   • CommentTimeJun 5th 2017
   • (edited Jun 5th 2017)
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexFYI: we have a [[Sandbox]] for this kind of thing. Right now it's occupied by some stuff of Urs, but you can create a new section and do your thing there. That would be better than creating a new page.

   FYI: we have a Sandbox for this kind of thing. Right now it’s occupied by some stuff of Urs, but you can create a new section and do your thing there. That would be better than creating a new page.

3. • CommentRowNumber3.
   • CommentAuthorRichard Williamson
   • CommentTimeJun 5th 2017
   • PermaLink
   Author: Richard Williamson
   Format: MarkdownItexI believe that Peter may have created it using SVG, and the instructions in the HowTo in that case are to put the code on its own page (because it is so long and unreadable).

   I believe that Peter may have created it using SVG, and the instructions in the HowTo in that case are to put the code on its own page (because it is so long and unreadable).

4. • CommentRowNumber4.
   • CommentAuthorRichard Williamson
   • CommentTimeJun 5th 2017
   • (edited Jun 5th 2017)
   • PermaLink
   Author: Richard Williamson
   Format: MarkdownItexOn my browser (an obscure but up to date webkit browser), by the way, the diagram does not render correctly. It is very unfortunate that SVG and MathML do not function nicely together at the present time, and that there is essentially no way at the present time to code nice mathematical figures, but I think the nLab's avoidance to date, for the most part, of SVG, in favour of other, more hackish but simpler, approaches has been wise. I would suggest either to code diagrams in the same, somewhat hackish, way as elsewhere on the nLab, or else just create the figure locally in TikZ or something, and then upload a vector graphic from this.

   On my browser (an obscure but up to date webkit browser), by the way, the diagram does not render correctly. It is very unfortunate that SVG and MathML do not function nicely together at the present time, and that there is essentially no way at the present time to code nice mathematical figures, but I think the nLab’s avoidance to date, for the most part, of SVG, in favour of other, more hackish but simpler, approaches has been wise.

   I would suggest either to code diagrams in the same, somewhat hackish, way as elsewhere on the nLab, or else just create the figure locally in TikZ or something, and then upload a vector graphic from this.

5. • CommentRowNumber5.
   • CommentAuthorTodd_Trimble
   • CommentTimeJun 5th 2017
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexOh, I see. Yes, SVG here seems to be a major pain in the neck. FWIW, it's easy to get what I think is an acceptable approximation to the diagram like so (see the Source for the code) $$\array{ O & \stackrel{f}{\to} & O' \\ \mathllap{h_0 = \theta(O)} \downarrow & & \downarrow \mathrlap{h^'_0 = \theta(O')} \\ G(O) & \stackrel{G(f)}{\to} & G(O') }$$

   Oh, I see.

   Yes, SVG here seems to be a major pain in the neck. FWIW, it’s easy to get what I think is an acceptable approximation to the diagram like so (see the Source for the code)

   $$\array{ O & \stackrel{f}{\to} & O' \\ \mathllap{h_0 = \theta(O)} \downarrow & & \downarrow \mathrlap{h^'_0 = \theta(O')} \\ G(O) & \stackrel{G(f)}{\to} & G(O') }$$
6. • CommentRowNumber6.
   • CommentAuthorPeter Heinig
   • CommentTimeJun 6th 2017
   • PermaLink
   Author: Peter Heinig
   Format: MarkdownItexThanks for the advice. Picture was created with TikZ, then converted, partly to get to know the nLab's technology and prepare for the article. Made conscious effort to first systematically read the HowTo, and, like predicted by Richard, just followed the instructions there which expressly say one should create a new page. Had first looked at Sandbox, but was turned away by a line at the top of its content saying not to change the content.

   Thanks for the advice. Picture was created with TikZ, then converted, partly to get to know the nLab’s technology and prepare for the article. Made conscious effort to first systematically read the HowTo, and, like predicted by Richard, just followed the instructions there which expressly say one should create a new page. Had first looked at Sandbox, but was turned away by a line at the top of its content saying not to change the content.

7. • CommentRowNumber7.
   • CommentAuthorPeter Heinig
   • CommentTimeJun 6th 2017
   • PermaLink
   Author: Peter Heinig
   Format: MarkdownItexTo be precise, I recognize the line in the sandbox says not to _erase_ rather than not to _change_. Took it to mean not to meddle in whatever way though and left the sandbox again.

   To be precise, I recognize the line in the sandbox says not to erase rather than not to change. Took it to mean not to meddle in whatever way though and left the sandbox again.

8. • CommentRowNumber8.
   • CommentAuthorTodd_Trimble
   • CommentTimeJun 6th 2017
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexThat line in the sandbox was put there recently by Urs and should be temporary. IMO you should feel free to add because the sandbox should be available to all; Urs can cut out and paste the exact thing he needs.

   That line in the sandbox was put there recently by Urs and should be temporary. IMO you should feel free to add because the sandbox should be available to all; Urs can cut out and paste the exact thing he needs.

9. • CommentRowNumber9.
   • CommentAuthorUrs
   • CommentTimeJun 6th 2017
   • PermaLink
   Author: Urs
   Format: MarkdownItexSorry, sure. Done now. [[Sandbox]] is free.

   Sorry, sure. Done now. Sandbox is free.