As of 11/6/2019, Capture One Version 12.1.4 is supported on Catalina (10.15.1). You are able to download the update here and read the release note here.
Please contact DT Support if you have any questions about the updates or want to report any bugs that you have found. We still recommend to test this on a computer that is not your daily driver to make sure all functions that you need are working; or make a bootable backup if necessary.
As a General Rule, You Should NOT Immediately Update Major OS Changes
As a general rule of thumb, it’s never a good idea to update to a new OS immediately after it is available. A lot of software, including the operating system itself, will have bugs, quirks, or poor performance until the initial “.0” issues are addressed (as in version 10.15.0). It almost always makes sense to wait (in the very least) until one “dot revision” of the operating system (e.g. 10.15.1) and until all your essential software has been updated and claim official support for the new OS. Even then, operating system upgrades should be treated as “major events” wherein you should be backing up your entire computer (we suggest SuperDuper) and testing the system extensively after the update (especially, but not only, if you will be using the computer for tethering.
Specifically About Capture One
Note that while many (but not all) users who decide to ignore this advice will find that C1 is running fine, that is very different than saying it is supported. Capture One is professional software that should only be used on supported configurations. Even if it launches and works fine initially you may find quirks, bugs, or even major issues in further use, and if you do there will be no official support response beyond “Catalina is not yet supported, please use a supported OS”.
As always, new operating systems mean lots of changes to the underlying code, libraries, and engines that Capture One leverages for its class-leading performance and stability. Phase One begins testing new operating systems months before they are released. However, Apple has a bad habit of making last-minute changes, even between the last beta and the released version. Therefore, extensive testing and tweaking is needed. We have no ETA for a new version of Capture One that will support Catalina, but of course it will come, and Digital Transitions will independently test it when it does.