Cap tables are generally pretty closely-guarded, and most startups would not let you see the full cap table.
That said, things you could ask for could be: the number of fully-diluted shares (to calculate your ownership), whether they have any convertible notes and what the terms are, what their last valuation was (pre or post-money), how much runway they have at current burn, whether existing investors have any liquidity preference, etc. They may not answer all of those, but they should be able to give you enough to know where you stand.
That said, things you could ask for could be: the number of fully-diluted shares (to calculate your ownership), whether they have any convertible notes and what the terms are, what their last valuation was (pre or post-money), how much runway they have at current burn, whether existing investors have any liquidity preference, etc. They may not answer all of those, but they should be able to give you enough to know where you stand.