Macbook Pro 13 inch Early 2015 keeps turning off on it's own.

Does this happen when the charger is connected or only when using it on the battery?

When does it turn off? While booting, or logging in, or after using it for a while (how long)?

Check the condition of the battery by Option-clicking on the battery icon on the menu bar. If the battery condition is anything other than "Normal", then the battery may need to be replaced. With macOS 10.15.5+, there will be no battery condition listed if it is "Normal", although the Battery System Preferences and the Apple System Profiler may show a "Normal" condition.

Try an SMC Reset.

Try running the Apple Diagnostics to see if any hardware issues are detected.

Boot into Internet Recovery Mode using Command + Option + R. As long as you boot to the installer for the same or newer version of macOS than you use when booting normally, then you should run Disk Utility First Aid on the hidden Container. Within Disk Utility you may need to click "View" and select "Show All Devices" before the hidden Container appears on the left pane of Disk Utility. Even if First Aid says everything is "Ok", click "Show Details" and scroll through the report to see if there are any unfixed errors are listed. If there are any unfixed errors listed, then you will need to perform a clean install of macOS by first erasing the whole physical drive followed by reinstalling macOS & restoring from a backup. Keep in mind erasing the drive will destroy all data on it so make sure to have a good backup first.

There is also a chance you could have a software issue causing the laptop to crash so try booting into Safe Mode.

myeloquentsoul Said:

"Macbook Pro 13 inch Early 2015 keeps turning off on its own."

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Troubleshooting a Mac in a Boot Loop:

Being consistent, it seems you are in a boot loop. So, refer to the following...

A. Reset your SMC and your NVRAM:

(Applies to Intel-Basel Macs Only) Sometimes changes (i.e. Installations) are made to the system and then settings (i.e. Networking) become corrupted, technically. So, reset both on your Mac. So, reset the SMC and reset the NVRAM or PRAM. It might take three tries. to fix this. So, be certain you have the time to do so.

Start With This:

• Reset NVRAM or PRAM on your Mac - Apple Support
• How to Reset the SMC of your Mac - Apple Support

B. Re-Mount the Drive:

Boot into Recovery Mode (Intel or Silicon) . You need to click the “Mount’ button to proceed. So, select the drives, and then click "Mount" Try rebooting once more. If of no success, then click unmount button, and then the mount button. Try rebooting once more. It looks dulled-out. So, if you cannot click it, then click the First Aid button to fix this volume.

and...

C. Install, or Restore to Access it:

If it is telling you kennel error,, then it is likely due to a corrupt update. So, either(A.) backup your Mac > erase the drive in Recovery Mode (Intel or Silicon) > install Catalina > Move a content using Migration Assistant. Or, (B.) just restore your Mac from a backup you created prior to this update. Didn't make a backup? If so, take this as a learning experience, knowing to always back up your Mac prior to making any major changes to it(such as an update. That way you can have something to restore your Mac from, should anything go wrong with the update.