How to change the tips of the 2-cells in xy-pic?

Question

I used the cmtip option in xypic, but this doesn't change the tips of the \xtwocells, and I have a lot of 2-cells. I am using cmtip because I want the tips in the diagrams to match the ones of the in-line arrows $A\to B$. It seems that the cmtip option is not compatible with the 2cell option. So how to change the tips of the 2-cells?

If this leads to also put any symbol (which can be oriented properly) in the place of the 2-cell. I would also like to know about that.

Here is a simple example. A square with a cell inside.

\documentclass{article}% 
\usepackage[all,2cell,cmtip]{xy}
\UseAllTwocells
\begin{document}
\[
\vcenter{\hbox{\xymatrix@!0@=15mm{
tl\ar[r]^-{t}\ar[d]_-{l}\xtwocell[rd]{}<>{2}&tr\ar[d]^-{r}\\
bl\ar[r]_-{b}&br
}}}
\]
\end{document}

Answer 1

\documentclass[12pt,a4paper]{article}

\usepackage{amssymb,amsmath}

\usepackage[all,cmtip]{xy}

\begin{document}

$$\xymatrix{
tl\ar[r]^t \ar[d]_l &tr\ar[d]^r\ar@{=>}[ld]^2\\
bl\ar[r]_b &br
}$$

\end{document}

Answer 2

Is a solution with tikz-cd Ok for you?

\documentclass{article}
\usepackage{tikz-cd}

\begin{document} 
    \[
    \begin{tikzcd}
        tl\ar{r}{t} \ar{d}[swap]{l} &tr \arrow[Rightarrow]{ld}{2}\arrow{d}{r} \\
        bl\ar{r}[swap]{b} &br
    \end{tikzcd}
    \] 
\end{document}