#cokernel

[ernestyalumni]

Rotman Advanced Modern Algebra

I find that in learning Algebraic Topology, for the Algebra part, picking up a few exercises and sections from Joseph Rotman's Advanced Modern Algebra is useful.  

http://www.amazon.com/Advanced-Modern-Algebra-Joseph-Rotman/dp/0130878685

Note that to show exactness of a short sequence of total length 5, you'll need to show injective and surjective for the first and last nontrivial homomorphism, and of course the exactness condition itself: im(i) = ker(h)