I believe this is a rendering problem. Also the mathematics symbols get
/tiny/; could rendering of mathematics made bigger, a little bolder, and
xymatrix diagram arrows made visible?

>> Can I use \LaTeX ? Let us try: $f: A\rightarrow B$ is a function
>
> MathJax ignores \LaTeX but renders the function correctly.
>
> (I tried with plain 'emacs -Q' on Emacs 30.)
>
>> $\xymatrix{ {A} \ar@{o->}[r] & {B} }$
>
> MathJax does not recognize this, hence the "Misplaced &" error.
>
> You have two options here: either (1) install the MathJax extension you
> mentioned or (2) make Org to use LaTeX for HTML.
>
> If you decide to go the MathJax/JavaScript route, please note that you need to
> use Emacs 29 or later, where Org uses MathJax 3 and not 2.
>

Thanks, I am on 28.2, the latest on Linux Mint archive; I think I shall
have to download and compile from gnu archives for the latest one. 

>> \Arr{f}{A}{B}
>

This is a problem; please see also below.

> MathJax does not recognize this either.
>
>> 2. The file exports perfectly to pdf:
>
> That happens because Org always uses LaTeX for PDF documents.  If you want it to
> use LaTeX for HTML too, see the OPTIONS above.
>
> Rudy

I have a huge amount of macros which are constantly used, especially
because the area of my work (Category Theory) demands use of plenty of
inline diagrams as well as displayed diagrams; for inline diagrams it is
best to have macros to speed up the typing. I believe you are saying
that while these are recognised by LaTeX for PDF documents, the html
converter just neglects them.

Firstly, is it possible to convert these macros to a form which is
acceptable by hrml converter?

I believe the answer is _Yes_, since the same commands between "$", "$"
works; but can this be automated? The suggestion is: would it be
possible to write some quick code to be used by the converter before
starting the process of conversion, so that a list of macros used is
made up, each of such macros automatically converted in a form usable
for html, and then used in the conversion disregarding the actual macro
file; the converted macros could then be placed somewhere in the header
of the converted html file.

With my regards and all the very best wishes,

partha