Finished horseshoe lemma.
Used classification of indecomposable reps of the A_n quiver to motivate the definition of homotopy operator.
Lemma: if phi_1, phi_2 : (P_i) -> (M_i) are chain maps inducing the same map on cohomology, and the (P_i) are projective, then there exists a homotopy operator.
Cor: if (P_i),(Q_i) are two projective resolutions, then they're homotopic. Hence when we apply a right exact functor to them, those complexes are still homotopic, so have the same cohomology.
Def. Injective modules.
Stated (but didn't prove) the analogue of the "TFAE" theorem we gave for projective modules.
Gave some examples injective Z-modules.
