File:DeltaFunctorLongExactSequence.png

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Summary

Description
English: A commutative diagram showing the long exact sequence attached to a short exact sequence obtained from a δ-functor.
Date
Source Own work using LaTex, dvipng, and inkscape
Author RobHar

Data file

The LaTeX code that produced this diagram is the following (minor improvements were made with inkscape):

\[\xymatrix{
            0\ar@{->}[r] & T^0(M^\prime)\ar@{->}[r] & T^0(M)\ar@{->}[r]
                   & T^0(M^{\prime\prime}) \ar `r[d] `_l[lll] ^{\delta^0} `^d[dlll] `^r[dll] [dll] \\
            & T^1(M^\prime)\ar@{->}[r] & \hspace{12pt}\cdots\hspace{12pt}\ar@{->}[r]
                   & T^n(M^{\prime\prime}) \ar `r[d] `_l[lll] ^{\delta^n} `^d[dlll] `^r[dll] [dll] \\
            &T^{n+1}(M^\prime)\ar@{->}[r] & T^{n+1}(M)\ar@{->}[r]
                   & T^{n+1}(M^{\prime\prime}) \ar `r[d] `_l[lll] ^{\delta^{n+1}} `^d[dlll] `^r[dll] [dll] \\
            & & \cdots &
}\]

Licensing

Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

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26 December 2008

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Date/TimeThumbnailDimensionsUserComment
current02:29, 27 December 2008Thumbnail for version as of 02:29, 27 December 2008939 × 475 (34 KB)wikimediacommons>RobHar{{Information |Description={{en|1=A commutative diagram showing the long exact sequence attached to a short exact sequence obtained from a δ-functor.}} |Source=Own work using LaTex and dvipng |Author=RobHar |Date=2008-12-26 |Permissi

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