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=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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

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    attribution share alike
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    Captions

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

    Items portrayed in this file

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    17 May 2026

    52,712 byte

    image/svg+xml

    8bb474855ef755db1462daeea5807b1870ac3248

    File history

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

    Date/TimeThumbnailDimensionsUserComment
    current17:09, 17 May 2026Thumbnail for version as of 17:09, 17 May 2026700 × 76 (51 KB)wikimediacommons>AscchrvalstrUploaded own work with UploadWizard

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