Triple Cohomology and the Galois Cohomology of Profinite Groups
Titel:
Triple Cohomology and the Galois Cohomology of Profinite Groups
Auteur:
Gildenhuys, D. Mackay, E.
Verschenen in:
Communications in algebra
Paginering:
Jaargang 1 (1974) nr. 6 pagina's 459-473
Jaar:
1974
Inhoud:
Given a cotriple 𝔾 = (G, ε, δ) on a category X and a functor E:XOpp→A into an abelian category A, there exists the cohomology theory of Barr and Beck: Hn(X, E) ε |A| (n ≥ 0, X ε |X|), ([1], p.249). Almost all the important cohomology theories in mathematics have been shown to be special instances of such a general theory (see [1], [2] and [3]). Usually E arises from an abelian group object Y in X in the following manner: it is the contravariant functor from X into the category Ab of abelian groups that associates to each object X in X the abelian group X(X, Y) of maps from X to Y. In such a situation we shall write Hn(X, Y)𝔾 instead of Hn(X, E)G. Barr and Beck [2] have shown that the Eilenberg-MacLane cohomology groups H̄n(π, A), n ≥ 2, can be re-captured as follows. One considers the free group cotriple 𝔾' on the category Gps of groups, which induces in a natural manner a cotriple 𝔾 on the category (Gps, π) of groups over a fixed group π.
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