Commutative diagrams and arrows

Question

I'm trying to make a commutative diagram with tikzcd. Here's what I get:

I want the hook from B to A to be upside down and the /simeq symbol over the arrow from C to D.

Sample code:

\documentclass[a4paper]{article}
\usepackage{amsmath}
\usepackage{tikz-cd}
\begin{document}
\[
\begin{tikzcd}
 A & B \arrow[l, hookrightarrow] \\
 D \arrow[u, hookrightarrow] & C \arrow[l, "\simeq"]
 \arrow[u, hookrightarrow]
\end{tikzcd}
\]
\end{document}

Answer 1

Here you are:

\documentclass[a4paper]{article}
\usepackage{amsmath}
\usepackage{tikz-cd}

\begin{document}

\[
\begin{tikzcd}
 A \arrow[r, hookleftarrow] & B\\
 D \arrow[u, hookrightarrow] & C \arrow[l, "\simeq", swap]
 \arrow[u, hookrightarrow]
\end{tikzcd}
\]

\end{document}