In homological algebra, the term 'ext' refers to a functor that provides a way to measure the extent to which a module fails to be projective. Specifically, 'Ext' is used to define derived functors of the Hom functor, which captures the idea of extensions of modules. This concept is essential for understanding the relationships between modules and their extensions, particularly in the context of left and right derived functors as well as universal properties that these derived functors satisfy.
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