Cohomology of Profinite Groups
نویسنده
چکیده
A directed set I is a partially ordered set such that for all i, j ∈ I there exists a k ∈ I such that k ≥ i and k ≥ j. An inverse system of groups is a collection of groups {Gi} indexed by a directed set I together with group homomorphisms πij : Gi −→ Gj whenever i ≥ j such that πii = idGi and πjk ◦ πij = πik. Let H be a group. We call a family of homomorphisms {ψi : H −→ Gi : i ∈ I} compatible if πijψi = ψj whenever i ≥ j. Given an inverse system of groups {Gi}i∈I we can define a new category with objects (H, (φi)i∈I) where H is a group and φi : H −→ Gi are homomorphisms such that H
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