Triple Cohomology and the Galois Cohomology of Profinite Groups
- 1 January 1974
- journal article
- research article
- Published by Taylor & Francis in Communications in Algebra
- Vol. 1 (6) , 459-473
- https://doi.org/10.1080/00927877408548716
Abstract
Given a cotriple 𝔾 = (G, ε, δ) on a category X and a functor E:X Opp→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)Keywords
This publication has 5 references indexed in Scilit:
- Free pro-C-groupsMathematische Zeitschrift, 1972
- Equational completion, model induced triples and pro-objectsJournal of Pure and Applied Algebra, 1971
- On pro-p-groups with a single defining relatorInventiones Mathematicae, 1968
- Pseudocompact algebras, profinite groups and class formationsJournal of Algebra, 1966
- Acyclic Models and TriplesPublished by Springer Nature ,1966