Direct sums and injective, projective, flat
Let
- projective if and only if both
and are projective - injective if and only if both
and are both injective - flat if and only if both
and are flat
Hints
- You'll likely want to exploit the isomorphism
- Also recall that tensor product commutes with direct sum
- You might also want to note that for a pair of morphisms
and , there is an isomorphism