Error in Tikz-cd package

Question

I am trying to draw the following commutative diagram.

I tried to start with the following commands,

\documentclass[12pt,a4paper,footinclude=true,headinclude=true,openany]{scrbook} 
\usepackage{tikz-cd,amsmath}


\begin{document}
\begin{tikzcd}
 D(T)=N(T)\oplus C_PT \arrow[l,shift left] [r]{www} & R(T)\oplus N(Q) \arrow [d]\arrow {r}& 1\\
  & d & 
\end{tikzcd}

\end{document}

But I am getting the following errors,

pgfkeys: I do not know the key '/tikz/l' and I am going to ignore it. Perhaps you misspelled it. \end{tikzcd}

Missing number, treated as zero \end{tikzcd}

pgfkeys: I do not know the key '/tikz/d' and I am going to ignore it. Perhaps you misspelled it. \end{tikzcd}

Questions:

1. How to correct these errors.

2. How to get the union symbol in that diagram in tikz-cd?

Answer 1

I can not read everything in your screen-shot but it must be somthing similar to this:

% arara: pdflatex

\documentclass{scrbook} 
\usepackage{tikz-cd}
\tikzset{%
    symbol/.style={%
        draw=none,
        every to/.append style={%
            edge node={node [sloped, allow upside down, auto=false]{$#1$}}}
    }
}
\begin{document}
    \begin{tikzcd}
        z=Q(P)\oplus N(P) \arrow[symbol=\supset]{d} 
        & y=\overline{R(T)}\oplus N(Q) \arrow[symbol=\supset]{d} 
        & z=Q(P)\oplus N(P) \arrow[symbol=\supset]{d} \\
        D(T)=N(T)\oplus C_P(T) \arrow{r}{T}\arrow[shift left]{d}{\widetilde{I-P}} 
        & R(T)\oplus N(Q) \arrow{r}{T^\dagger}\arrow[shift left]{d}{\widetilde{Q}}
        & N(T)\oplus C_P(T) \arrow[shift left]{d}{\widetilde{I-P}} \\
        C_P(T)=D(T) \cap N(P) \arrow{r}{\widetilde{T}}\arrow[shift left]{u}{i} 
        & R(T) \arrow{r}{\widetilde{T}^{-1}}\arrow[shift left]{u}{j}
        & C_p(T)=R(T^\dagger T) \arrow[shift left]{u}{i}
    \end{tikzcd}
\end{document}