Hi there! I understand that the JW Library app won’t start on your Mac running OS X 10.15 Catalina. Let's work together to get this sorted out.

First, I want to check a quick detail: Are you trying to run the official JW Library app designed specifically for macOS, or are you using an iOS version of the app on your Mac?

Here’s why I ask: JW Library is officially compatible with macOS only on Macs that have an M1 chip or newer. Since you mentioned running macOS 10.15 Catalina, which often means an Intel-based Mac, the native macOS version might not be supported. Users often resort to workarounds like using the iOS app through emulators or other methods, which sometimes causes startup issues.

If you are on an Intel Mac with Catalina, here are some steps you can try:

1. Ensure you have the latest version of JW Library: Sometimes, installing the most recent update (if available) can resolve issues.

2. Clear the app cache:
- Go to Finder.
- In the menu bar, click 'Go' > 'Go to Folder…'
- Enter ~/Library/Containers/ and find the folder related to JW Library.
- Delete any cache or temporary files you find inside.

3. Try running the app as an administrator: Right-click (or Control-click) the JW Library app icon and choose 'Open' to bypass some security restrictions.

4. Check if any macOS security settings are blocking the app: Go to System Preferences > Security & Privacy > General tab, and see if there is any message about blocking the app from running, then allow it.

If these steps don’t help, please confirm if you are using an Intel Mac or an M1 Mac and whether you installed the app from the Mac App Store or through another method. That way, I can suggest alternative options to access JW Library, such as running the iOS version with a compatible method or other solutions.

Looking forward to your reply so we can get JW Library running smoothly on your Mac!