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File:Two long exact sequences.svg

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Summary

Description
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=WzAsMTgsWzAsMCwiMCJdLFsxLDAsIkYoQV8xKSJdLFswLDEsIjAiXSxbMSwxLCJGKEFfMikiXSxbMiwwLCJGKEJfMSkiXSxbMiwxLCJGKEJfMikiXSxbMywwLCJGKENfMSkiXSxbMywxLCJGKENfMikiXSxbNCwwLCJSXjFGKEFfMSkiXSxbNCwxLCJSXjFGKEFfMikiXSxbNSwwLCJSXjFGKEJfMSkiXSxbNSwxLCJSXjFGKEJfMikiXSxbNiwwLCJSXjFGKENfMSkiXSxbNiwxLCJSXjFGKENfMikiXSxbNywwLCJSXjJGKEFfMSkiXSxbNywxLCJSXjJGKEFfMikiXSxbOCwwLCJcXGNkb3RzIl0sWzgsMSwiXFxjZG90cyJdLFswLDFdLFsyLDNdLFsxLDMsIkYoXFxhbHBoYSkiLDJdLFsxLDQsIkYoZl8xKSJdLFszLDUsIkYoZl8yKSJdLFs0LDUsIkYoXFxiZXRhKSIsMl0sWzQsNiwiRihnXzEpIl0sWzUsNywiRihnXzIpIl0sWzYsNywiRihcXGdhbW1hKSIsMl0sWzYsOF0sWzcsOV0sWzgsOSwiUl4xRihcXGFscGhhKSIsMl0sWzgsMTAsIlJeMUYoZl8xKSJdLFs5LDExLCJSXjFGKGZfMikiXSxbMTAsMTEsIlJeMUYoXFxiZXRhKSIsMl0sWzEwLDEyLCJSXjFGKGdfMSkiXSxbMTEsMTMsIlJeMUYoZ18yKSJdLFsxMiwxMywiUl4xRihcXGdhbW1hKSIsMl0sWzEyLDE0XSxbMTMsMTVdLFsxNCwxNSwiUl4yRihcXGFscGhhKSIsMl0sWzE0LDE2LCJSXjJGKGZfMSkiXSxbMTUsMTcsIlJeMkYoZl8yKSJdXQ==
\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

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w:en:Creative Commons
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Captions

A commutative diagram between two long exact sequences induced by right-derived functors on two commuting short exact sequences

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17 May 2026

52,712 byte

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8bb474855ef755db1462daeea5807b1870ac3248

File history

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Date/TimeThumbnailDimensionsUserComment
current15:09, 17 May 2026Thumbnail for version as of 15:09, 17 May 2026700 × 76 (51 KB)wikimediacommons>AscchrvalstrUploaded own work with UploadWizard
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