How can I write a tower of unions?

Question

Here is the figure I want to write on latex:

Could anyone tell me what is the correct name of this figure and how to form it in latex please?

Sandy G · Accepted Answer

You can place the entries in a matrix using the amsmath package:

documentclass{article}

usepackage{amsmath}

begin{document}

[
begin{matrix}
vdots & & vdots & & vdots
cup & & cup & & cup
L_3(I_1) & subset & L_3(I_2) & subset & L_3(I_3) & subset & cdots
cup & & cup & & cup
L_2(I_1) & subset & L_2(I_2) & subset & L_2(I_3) & subset & cdots
cup & & cup & & cup
L_1(I_1) & subset & L_1(I_2) & subset & L_1(I_3) & subset & cdots
end{matrix}
]

end{document}

If you want to reduce the spacing between columns, you can add setlengtharraycolsep{1.5pt} (or whatever spacing seems right to you) before begin{matrix}.

It's best to enclose the adjustment in begingroup..endgroup to ensure you don't affect spacing in the rest of your document:
[
begingroup
setlengtharraycolsep{1.5pt}
begin{matrix}
vdots & & vdots & & vdots
cup & & cup & & cup
L_3(I_1) & subset & L_3(I_2) & subset & L_3(I_3) & subset & cdots
cup & & cup & & cup
L_2(I_1) & subset & L_2(I_2) & subset & L_2(I_3) & subset & cdots
cup & & cup & & cup
L_1(I_1) & subset & L_1(I_2) & subset & L_1(I_3) & subset & cdots
end{matrix}
endgroup
]

egreg · Answer

You can see that cup is not a rotated subset symbol.
In order to get the standard spacing around relation symbols, it's better to set arraycolsep to zero and rely on TeX's own method, by adding {} fore and aft.
documentclass{article}
usepackage{amsmath,array,graphicx}

newcommand{rotsubset}{rotatebox[origin=c]{90}{$subset$}}

begin{document}

begin{equation*}
setlength{arraycolsep}{0pt}
begin{array}{ *{7}{ >{{}}c<{{}} } }
vdots     &         & vdots     &         & vdots 
rotsubset &         & rotsubset &         & rotsubset 
L_3(I_1)   & subset & L_3(I_2)   & subset & L_3(I_3) & subset & cdots 
rotsubset &         & rotsubset &         & rotsubset 
L_2(I_1)   & subset & L_2(I_2)   & subset & L_2(I_3) & subset & cdots 
rotsubset &         & rotsubset &         & rotsubset 
L_1(I_1)   & subset & L_1(I_2)   & subset & L_1(I_3) & subset & cdots
end{array}
end{equation*}

end{document}

Jendrik Stelzner · Answer

Your image is a commutative diagram of inclusions, so you may want to use the package tikz-cd.
documentclass{scrartcl}

usepackage{tikz-cd}

begin{document}
[
  begin{tikzcd}
    vdots
    &
    vdots
    &
    vdots
    &
    {}
    
    L_3(I_1)
    arrow[phantom]{u}[rotate=90]{subset}
    arrow[phantom]{r}{subset}
    &
    L_3(I_2)
    arrow[phantom]{u}[rotate=90]{subset}
    arrow[phantom]{r}{subset}
    &
    L_3(I_3)
    arrow[phantom]{u}[rotate=90]{subset}
    arrow[phantom]{r}{subset}
    &
    cdots
    
    L_2(I_1)
    arrow[phantom]{u}[rotate=90]{subset}
    arrow[phantom]{r}{subset}
    &
    L_2(I_2)
    arrow[phantom]{u}[rotate=90]{subset}
    arrow[phantom]{r}{subset}
    &
    L_2(I_3)
    arrow[phantom]{u}[rotate=90]{subset}
    arrow[phantom]{r}{subset}
    &
    cdots
    
    L_1(I_1)
    arrow[phantom]{u}[rotate=90]{subset}
    arrow[phantom]{r}{subset}
    &
    L_1(I_2)
    arrow[phantom]{u}[rotate=90]{subset}
    arrow[phantom]{r}{subset}
    &
    L_1(I_3)
    arrow[phantom]{u}[rotate=90]{subset}
    arrow[phantom]{r}{subset}
    &
    cdots
  end{tikzcd}
]
end{document}

How can I write a tower of unions?

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