Definition of FI


I have a question regarding the definition of FI. In this case a PE company that both invests in x number of companies (in different sectors) but also has the operational management of x number of companies (approx. 50/50 in CO2e). In this case, should one apply as FI and is category 1-14 still voluntary, even though 50% of the emissions are found within these categories?

Thanks in advance!

The same question applies for a real estate company that invest in other real estate companies (investment stands for more than 5% of the revenue), are you then considered to be a FI according to the SBTi definition?