File:Two long exact sequences.svg
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Summary
| DescriptionTwo long exact sequences.svg |
English: A commutative diagram between two long exact sequences induced by right-derived functors on two commuting short exact sequences
中文(简体):两个由右导出函子在两个交换的短正合序列上诱导的长正合序列之间的交换图表 |
| Date | |
| Source | Own work |
| Author | Ascchrvalstr |
Source code
\documentclass[crop,tikz,convert={outext=.svg,command=\unexpanded{pdf2svg \infile\space\outfile}},multi=false]{standalone}
\usepackage{tikz-cd}
\tikzcdset{arrow style=tikz, diagrams={>=stealth}}
\begin{document}
% https://q.uiver.app/#q=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
\begin{tikzcd}
0 & {F(A_1)} & {F(B_1)} & {F(C_1)} & {R^1F(A_1)} & {R^1F(B_1)} & {R^1F(C_1)} & {R^2F(A_1)} & \cdots \\
0 & {F(A_2)} & {F(B_2)} & {F(C_2)} & {R^1F(A_2)} & {R^1F(B_2)} & {R^1F(C_2)} & {R^2F(A_2)} & \cdots
\arrow[from=1-1, to=1-2]
\arrow["{F(f_1)}", from=1-2, to=1-3]
\arrow["{F(\alpha)}"', from=1-2, to=2-2]
\arrow["{F(g_1)}", from=1-3, to=1-4]
\arrow["{F(\beta)}"', from=1-3, to=2-3]
\arrow[from=1-4, to=1-5]
\arrow["{F(\gamma)}"', from=1-4, to=2-4]
\arrow["{R^1F(f_1)}", from=1-5, to=1-6]
\arrow["{R^1F(\alpha)}"', from=1-5, to=2-5]
\arrow["{R^1F(g_1)}", from=1-6, to=1-7]
\arrow["{R^1F(\beta)}"', from=1-6, to=2-6]
\arrow[from=1-7, to=1-8]
\arrow["{R^1F(\gamma)}"', from=1-7, to=2-7]
\arrow["{R^2F(f_1)}", from=1-8, to=1-9]
\arrow["{R^2F(\alpha)}"', from=1-8, to=2-8]
\arrow[from=2-1, to=2-2]
\arrow["{F(f_2)}", from=2-2, to=2-3]
\arrow["{F(g_2)}", from=2-3, to=2-4]
\arrow[from=2-4, to=2-5]
\arrow["{R^1F(f_2)}", from=2-5, to=2-6]
\arrow["{R^1F(g_2)}", from=2-6, to=2-7]
\arrow[from=2-7, to=2-8]
\arrow["{R^2F(f_2)}", from=2-8, to=2-9]
\end{tikzcd}
\end{document}
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
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- 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.
Captions
A commutative diagram between two long exact sequences induced by right-derived functors on two commuting short exact sequences
两个由右导出函子在两个交换的短正合序列上诱导的长正合序列之间的交换图表
Items portrayed in this file
depicts
17 May 2026
52,712 byte
image/svg+xml
8bb474855ef755db1462daeea5807b1870ac3248
File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 15:09, 17 May 2026 | 700 × 76 (51 KB) | wikimediacommons>Ascchrvalstr | Uploaded own work with UploadWizard |
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| Width | 525.369pt |
|---|---|
| Height | 56.901pt |
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