A projective resolution is an exact sequence of modules and module homomorphisms that starts with a projective module and leads to the zero module. This concept is vital in homological algebra, as it helps to compute derived functors, such as Ext and Tor, and gives insight into the structure of modules over a ring. In the context of cohomology of groups, projective resolutions allow for the examination of group cohomology through the lens of projective modules, providing deeper understanding of their relationships and properties.
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