Jump to content

File:DeltaFunctorLongExactSequence.png

Page contents not supported in other languages.
This is a file from the Wikimedia Commons
From Wikipedia, the free encyclopedia

Original file (939 × 475 pixels, file size: 34 KB, MIME type: image/png)

This math image could be re-created using vector graphics as an SVG file. This has several advantages; see Commons:Media for cleanup for more information. If an SVG form of this image is available, please upload it and afterwards replace this template with {{vector version available|new image name}}.


It is recommended to name the SVG file “DeltaFunctorLongExactSequence.svg”—then the template Vector version available (or Vva) does not need the new image name parameter.

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.

Captions

Add a one-line explanation of what this file represents

Items portrayed in this file

depicts

26 December 2008

image/png

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current00:29, 27 December 2008Thumbnail for version as of 00:29, 27 December 2008939 × 475 (34 KB)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

The following page uses this file: