Please capitalize where necessary: in 1939 he examined the homology of a compact lie group.
A: In 1939 he examined the homology of a compact Lie group.

Please capitalize where necessary: the series of games that each pair of backgammon players play against each other in is known as a backgammon match.
A: The series of games that each pair of backgammon players play against each other in is known as a backgammon match.

Please capitalize where necessary: unix-on-intel players work on a common binary format
A: Unix-on-Intel players work on a common binary format

Please capitalize where necessary: these metrics are always associated with objectives.
A:
These metrics are always associated with objectives.