Strangely, I've never heard Ext functors referred to by any other name, and so I'm not sure what "Ext" actually means. The only thing I can think of that "Ext" might stand for is "Exterior", which makes a little bit of sense. Does anybody know the meaning and/or history of the term?
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$\begingroup$For given $A,B$ we call a short sequence of the form $$0\to A\to C\to B\to 0$$ an extension of $A$ by $B$, the trivial extension being that with $C=A\oplus B$. The Ext functor measures (and gets its name from this) how many inequivalent extensions there are (with equivalence defined by isomorphism of short exact sequences that are the identity on $A$ and $B$).
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