Objective-C? That seems like an odd choice, did they want to attract iOS developers? (I know someone ported the mobile game Angry Birds to PSP at some point). Do you have more information about this?
https://apple.slashdot.org/story/10/11/25/0432204/Sony-Adopt...
https://www.slashgear.com/sony-snap-connected-device-app-fra...
And for completness here are some articles about the C# SDK,
https://venturebeat.com/games/ps-vita-sdk/
https://www.codeproject.com/Articles/535325/Hello-World-on-t...