This is a new rap on the oldest of stories — Functors on abelian categories. If the functor is left exact You can derive it and that's a fact But first you must have enough injective Objects in the category to stay active. If that's the case — no time to lose; Resolve injectively any way you choose. Apply the functor and don't be sore — The sequence ain't exact no more. Here comes the part that is the most fun, Sir, Take homology to get the answer. On resolution it don't depend: All are chain homotopy equivalent. Hey, Mama, when your algebra shows a gap Go over this Derived Functor Rap.
Это мой старый друг Павлик забавлялся...1988 год
Paul Bressler
This is a new rap on the oldest of stories —
Functors on abelian categories.
If the functor is left exact
You can derive it and that's a fact
But first you must have enough injective
Objects in the category to stay active.
If that's the case — no time to lose;
Resolve injectively any way you choose.
Apply the functor and don't be sore —
The sequence ain't exact no more.
Here comes the part that is the most fun, Sir,
Take homology to get the answer.
On resolution it don't depend:
All are chain homotopy equivalent.
Hey, Mama, when your algebra shows a gap
Go over this Derived Functor Rap.