How do I categorize building improvements to a leased business space? What type of "expense" category do I list them in? For example, I paid for new carpet to be installed into my business offices. Also, does this affect any other accounts... equity, liability, or assets?

Is this an accounting class question or real life scenario? Depend on the lease itself. Is it a operation lease or a capital lease? If it's a operation lease, it can be categorized as expenses. If capital lease, put it in leasehold improvement. The accounts that it affects depends on how you paid for the item, could be cash, or payable.