[Tex/LaTex] How to add two sided arrow in this chain of commutative diagram

commutative-diagramstikz-arrowstikz-cd

I want to build a chain of commutative diagram

I did get the code here for building the commutative diagram. This is the code.

\documentclass[12pt,twoside,a4paper]{report}
\usepackage{tikz-cd}
%\newcommand{\nospaceperiod}{\makebox[0pt][l]{\,}}
\begin{document}
\[
\begin{tikzcd}
V_1 \arrow{r} \arrow{d}{f_1} &
  V_2    \arrow{r} \arrow{d}{f_2} &
 \cdots \arrow{r} &
  V_{n-1} \arrow{r}    \arrow{d}{f_{n-1}} &
  V_n \arrow{d}{f_n}
\\
W_1 \arrow{r} &
 W_2      \arrow{r} &
 \cdots      \arrow{r} &
  W_{n-1} \arrow{r} &
W_n
\end{tikzcd}
\]
\end{document}

which gives this output

enter image description here

I am almost done. I just want to know what do I change in \arrow{r} to make the right arrow to be two sided arrow or hook arrow or curved arrow.

I want output to look like these

chain of Commutative diagram

Curved arrow

Please share some manual that gives different keywords for different kind of arrows.

Best Answer

For two sided arrow, simply replace it by: \arrow[<->]{r}.

To bend the arrow, use: \arrow[bend right]{r} or \arrow[bend left]{r}

Use \arrow[bend right]{rr}to point the curved arrow to next but one variable.

To get the output as in last image, use this code

\documentclass{report}
\usepackage{tikz-cd,bbm,amsmath,amssymb}

\begin{document}
\[
\begin{tikzcd}
I    \arrow{r}{s}
     \arrow[bend right]{rr}{\mathbbm{1}} &
X^c  \arrow{r}{p}                        &
I 
\end{tikzcd}
\]
\end{document}
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