Calcul des satellites et présentations des bimodules à l’aide des carrés exacts. \(2^ e\) partie. (French) Zbl 0574.18007

This is a rather long paper published through two subsequent issues of the same journal [part I, ibid. 24, 299-330 (1983; Zbl 0533.18007)]. The first half of the paper develops the notion of an exact square, which generalizes to arbitrary categories the techniques of exact sequences known for abelian categories. In particular, the authors compute in terms of exact squares the satellites of a bimodule \((=\) distributor, profunctor).
In the second half, the general theory is applied at first to some classical situations, like the functors \(Ext^ n\) and the corresponding long exact sequence. This includes the computation of Ext for chain complexes. An interesting point is the presentation of a bimodule on the category of small categories, whose corresponding satellites provide non- abelian cohomology theories of arbitrary order.
Reviewer: F.Borceux


18G10 Resolutions; derived functors (category-theoretic aspects)
18G15 Ext and Tor, generalizations, Künneth formula (category-theoretic aspects)
18G35 Chain complexes (category-theoretic aspects), dg categories
18G50 Nonabelian homological algebra (category-theoretic aspects)
18C15 Monads (= standard construction, triple or triad), algebras for monads, homology and derived functors for monads
18E25 Derived functors and satellites (MSC2010)
55U15 Chain complexes in algebraic topology


Zbl 0533.18007
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