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The video tutorial discusses analyzing Co Colonel of I star n minus 1 through free resolution. A free resolution of an abelian group is defined as an exact sequence where the kernel is equal to the image, resulting in trivial homology groups. The exact sequence, found on page 194 of Hatcher, is constructed to form the free resolution. Each component, f 2 f 1 f 0, is free. By applying the home, the arrows are reversed, resulting in a cochain complex.