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Possible Answers: EXT.
Random information on the term “EXT”:
In mathematics, the Ext functors of homological algebra are derived functors of Hom functors. They were first used in algebraic topology, but are common in many areas of mathematics. The name “Ext” comes from group theory, as the Ext functor is used in group cohomology to classify abelian group extensions.
Let R be a ring and let ModR be the category of modules over R. Let B be in ModR and set T(B) = HomR(A,B), for fixed A in ModR. This is a left exact functor and thus has right derived functors RnT. The Ext functor is defined by
This can be calculated by taking any injective resolution
and computing
Then (RnT)(B) is the homology of this complex. Note that HomR(A,B) is excluded from the complex.
An alternative definition is given using the functor G(A)=HomR(A,B). For a fixed module B, this is a contravariant left exact functor, and thus we also have right derived functors RnG, and can define
This can be calculated by choosing any projective resolution