File:Two long exact sequences2.png

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Two_long_exact_sequences2.png(660 × 101 pixels, file size: 4 KB, MIME type: image/png)

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Transferred from en.wikipedia to Commons by Maksim.

The original description page was here. All following user names refer to en.wikipedia.

Image of two long exact sequences, to be used for derived functor. Produced with Xy-pic using the following source code. Both the image and the source code are in the public domain.


% Produce a postscript file from this input with tex and dvips.

% Loading the XY-Pic package:
\input xy
\xyoption{all}

% Using postscript driver for smoother curves
\xyoption{ps}
\xyoption{dvips}

% No need for page numbers
\nopagenumbers

$$
\xymatrix{ %Our diagram is a 2x7 matrix
 0\ar[r]& F(A)\ar[d]_{\eta_A}\ar[r]^{F(f)} & F(B)\ar[d]_{\eta_B}\ar[r]^{F(g)}&
 F(C)\ar[d]_{\eta_C}\ar[r]&R^1\!F(A)\ar[d]_{R^1\!\eta_A}\ar[r]^{R^1\!F(f)} & R^1\!F(B)\ar[d]_{R^1\!\eta_B}\ar[r]^{R^1\!F(g)}&
 R^1\!F(C)\ar[d]_{R^1\!\eta_C}\ar[r]&R^2F(A)\ar[d]_{R^2\!\eta_A}\ar[r]^{R^2\!F(f)}&\cdots\\
 0\ar[r]& G(A)\ar[r]^{G(f)} & G(B)\ar[r]^{G(g)}& G(C)\ar[r]&R^1\!G(A)\ar[r]^{R^1\!G(f)} & R^1\!G(B)\ar[r]^{R^1\!G(g)}& R^1\!G(C)\ar[r]&R^2\!G(A)\ar[r]^{R^2\!G(f)}&\cdots
}
$$

\end


GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.
w:en:Creative Commons
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This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
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This licensing tag was added to this file as part of the GFDL licensing update.
date/time username edit summary
03:31, 19 November 2004 en:User:Quadell (?)
03:31, 19 November 2004 en:User:Quadell ({{GFDL}})
02:03, 18 January 2004 en:User:AxelBoldt
02:00, 18 January 2004 en:User:AxelBoldt

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Date/TimeThumbnailDimensionsUserComment
current20:59, 18 March 2006Thumbnail for version as of 20:59, 18 March 2006660 × 101 (4 KB)wikimediacommons>MaksimLa bildo estas kopiita de wikipedia:en. La originala priskribo estas: Image of two long exact sequences, to be used for derived functor. Produced with Xy-pic using the following source code. Both the image and the source code are in the public domain

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