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For a finite group $G$, the so-called $G$-Mackey functors form an abelian category $M(G)$ that has many applications in the study of $G$-equivariant stable homotopy. One would expect that the derived category $D(M(G))$ would be similarly important as the "homological" counterpart of the $G$-equivariant stable homotopy category.
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Note to my paper: ``A diagram of the functors of the two-valued propositional calculus''. [PDF]
Thomas W. Scharle
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Peter Freyd, Abeliwi Categories. An Introduction to the Theory of Functors (Harper and Row, 1964), xi+164 pp., $7.00. [PDF]
John Howie
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On the propositional calculus with a variable functor, $C \delta pC \delta Np \delta q$ [PDF]
Shôtarô Tanaka
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