Relative derived functors

Derived Functors

Relative Approximations and Maschke functors

The notion of approximations relative to a functor is introduced and several characterizations of relative (dual) Maschke functors are given by using them. As an application, the injective objects in the category of comodules over a coring are described.

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...

Regular functors and relative realisability categories

The relative realizability toposes that Awodey, Birkedal and Scott introduced in [1] satisfy a universal property that involves regular functors to other categories. We use this universal property to define what relative realizability categories are, when based on other categories than of the topos of sets. This paper explains the property and gives a construction for relative realizability cat...