Group derived functors

Derived Functors

Covering Functors, Skew Group Categories and Derived Equivalences

Abstract. Let G be a group of automorphisms of a category C. We give a definition for a functor F : C → C to be a G-covering and three constructions of the orbit category C/G, which generalizes the notion of a Galois covering of locally finitedimensional categories with group G whose action on C is free and locally bonded. Here C/G is defined for any category C and does not require that the act...

Composite Cotriples and Derived Functors

The main result of [Barr (1967)] is that the cohomology of an algebra with respect to the free associate algebra cotriple can be described by the resolution given by U. Shukla in [Shukla (1961)]. That looks like a composite resolution; first an algebra is resolved by means of free modules (over the ground ring) and then this resolution is given the structure of a DG-algebra and resolved by the ...

Non-additive Functors, Their Derived Functors, and the Suspension Homomorphism.

3E. L. Post, J. Symb. Logic, 12, 1-11, 1947. 4In the sense of Post, the word problem for Z is reducible to that for sp (2:). 5 W. Magnus, Math. Annalen, 106, 295-307, 1932. 6 DanaScott, abstract, J. Symb. Logic, 21, 111-112, 1956. 7Marshall Hall, J. Symb. Logic, 14, 115-118, 1949. 8 G. Higman, B. H. Neumann, and H. Neumann, J. London Math. Soc., 24, 247-254, 1949. 9 As defined, UG, Part I, p. 2...

Group Functors in Plain English

ion. It is more a descent to the mesosphere. For simplicity of discussion, we shall stick to biset functors, though variants of the material apply also to other kinds of group functors. In our account of biset functors, we mentioned that the abstraction here is rather similar to the abstraction behind the notion of ratios: just as the Greeks moved towards abstract ratios in place of ratios of p...