File:Braid category inverse hexagon.svg
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Size of this PNG preview of this SVG file: 688 × 188 pixels. Other resolutions: 320 × 87 pixels | 640 × 175 pixels | 1,024 × 280 pixels | 1,280 × 350 pixels | 2,560 × 700 pixels.
Original file (SVG file, nominally 688 × 188 pixels, file size: 30 KB)
Summary
| Description |
English: svg version of CategoryBraiding-03.png |
| Date | |
| Source | Own work |
| Author | IkamusumeFan |
| Other versions |
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LaTeX Source Code
% One needs PDF2SVG to generate the SVG graph.
% Author: Ika
% Update Date: 11/22/2014
\documentclass{amsart}
\usepackage[paperwidth=550px, paperheight=150px, top=-12px, left=0px, right=0px, bottom=0px]{geometry}
\usepackage{amsmath,amssymb,nopageno}
\usepackage[all]{xy}
\begin{document}
\Huge
\[
\xymatrix{
& (A \otimes B) \otimes C \ar^{\gamma}[r] & C \otimes (A \otimes B) \ar^{\alpha^{-1}}[dr] & \\
A \otimes (B \otimes C) \ar^{\alpha^{-1}}[ur] \ar_{1 \otimes \gamma}[dr] & & & (C \otimes A) \otimes B \\
& A \otimes (C \otimes B) \ar_{\alpha^{-1}}[r] & (A \otimes C) \otimes B \ar_{\gamma \otimes 1}[ur] &
}
\]
\end{document}
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This image shows some kind of formula that could be converted to TeX. Storing formulas as images makes it harder to change them. TeX also helps making sure that they all use the same font and size. A replacement has been proposed: In your article, replace the image with: <math>\begin{array}{c}
(A \otimes B) \otimes C \xrightarrow{\quad \gamma \quad} C \otimes (A \otimes B)\\
{}^{\alpha^{-1} }\nearrow \quad \quad \quad \quad \quad \quad \quad \searrow^{\alpha^{-1} } \\
A \otimes (B \otimes C) \quad \quad \quad \quad \quad \quad \quad (C \otimes A) \otimes B \\
{}_{1 \otimes \gamma}\searrow \quad \quad \quad \quad \quad \quad \quad \nearrow_{\gamma \otimes 1} \\
A \otimes (C \otimes B) \xrightarrow[\quad \alpha^{-1} \quad]{} (A \otimes C) \otimes B
\end{array}</math>
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![{\displaystyle {\begin{array}{c}(A\otimes B)\otimes C{\xrightarrow {\quad \gamma \quad }}C\otimes (A\otimes B)\\{}^{\alpha ^{-1}}\nearrow \quad \quad \quad \quad \quad \quad \quad \searrow ^{\alpha ^{-1}}\\A\otimes (B\otimes C)\quad \quad \quad \quad \quad \quad \quad (C\otimes A)\otimes B\\{}_{1\otimes \gamma }\searrow \quad \quad \quad \quad \quad \quad \quad \nearrow _{\gamma \otimes 1}\\A\otimes (C\otimes B){\xrightarrow[{\quad \alpha ^{-1}\quad }]{}}(A\otimes C)\otimes B\end{array}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a410fcc6ffbf4d8d02844be3ddceadb4afbfa880)
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 00:12, 23 November 2014 | | 688 × 188 (30 KB) | wikimediacommons>IkamusumeFan | User created page with UploadWizard |
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