will AMD Radeon HD 6770M 512 MB work with catalina or no?

Ah.....no... it will not...

Mojave (and Catalina) will only support Metal Capable video/graphics cards, and yours doesn't qualify. not even close.

As well, if you're using a Mac Pro/iMac Pro/iMac, only ones from a certain year and above qualify. In the case of Catalina, it's

Late 2012 and up for the iMac, iMac Pro it's 2017, and for the Mac pro it's Late 2013 and 2019.

you can find out what year your iMac was made by going to "About this Mac" under the large Apple icon at the top left of your

screen. it should give you a rough model number. if you go to everymac.com and type that in under "search" it will tell you what model and year of iMac you have

good luck

john b

FWIW, there is more involved than just video card incompatibility

in terms of upgrading to Catalina. There are also other hardware

limitations that prevent it as well.