Is there a way to map the bank's expense categories to the ones I use in quicken?

How are you importing these transactions?

For Direct Connect/Express Web Connect/Web Connect, Quicken doesn't get a category from the financial institution.  The OFX protocol that is used, doesn't even allow for a category.  The only format that allows this is QIF.

Quicken puts in categories based on either "guesses" using the payee/memo or a list of merchants (when automatic categorization is on) or by your renaming rules.

So basically #2 is "automatic" because Quicken never gets this information (and you should create renaming rules/memorized payees (which fill in the category) to get what you want.  And #1 isn't possible because of the same reason.

@DarthVogel Quicken is over 35 years old, and yes it shows it age.
At its heart is a database that has long gone unsupported, and even though it is easy to say that the application should have been written so that the database could easily be replaced, in practice that isn't going to be the case.  And that isn't the only part of Quicken like this.  The Tax Planner, Lifetime Planner, and business forms GUIs all come from the late 1990s when Microsoft was push the "Desktop as the web".  They are actually ActiveX web pages.

And then there are some "poor choices" (in my opinion) in the not so distant past, for instance the "fake main window".

So why not a total rewrite?
Because people, include developers (or maybe especially developers) way under estimate how many features there are in Quicken and the customers always expect everyone of them to remain "unchanged", but "working the way they want".  Intuit (Intuit sold Quicken to Quicken Inc a few years ago) tried that with Quicken Mac to this day Quicken Mac isn't back to the same level of features it had in Quicken for Mac 2007 when the rewrite started.  They didn't even make any money on the Mac product from 2008 to about 2014.  And Quicken Windows had more features and continued to get more features over the years.  No matter how painful it is to maintain the old code, I think they have learned their lesson.  It is still what pays the bills.

And BTW one of the major problems isn't even Quicken Inc's (or even Intuit which Quicken Inc still pays to maintain Express Web Connect and Direct Connect with the financial institutions), it is with the fact that the financial will not adopt a standard on how to download transactions.   The EU have long since forced their financial institutions to support one or both of two standards (one being the OFX standard that Quicken was first built on, but only got to about 4,500 financial institutions and is less than half of that today), but in the US (and Canadian) we are "free" free to have a chaotic system of companies like Intuit making "agreements" with financial institutions on how they might download transactions from their website.  And one of the biggest problems there is just how to log in since the same "interactive/security blocking/non standard) that they put up for the users is of course pushed on these "agreements" and changes all the time.