CompletedGroupAlgebra.AllFiniteFunctoriality
This module develops completed group algebras through finite quotient stages, transition maps, coefficient change, augmentation, comparison maps, and inverse-limit topology.
Comap
The inverse image of an open-finite quotient of \(H\) along a continuous homomorphism \(G\to H\), regarded as an open-finite quotient of the profinite group \(G\). This is the i...
GroupLike
The completed functorial map sends the group-like element attached to \(g\) to that of \(\varphi(g)\).
InClassNaturality
Completed Group Algebra / All Finite Functoriality / Within a Class Naturality.
Map
In Lemma 5.3.5(e), map construction, a continuous homomorphism of profinite groups \(\varphi : G \to H\) induces a continuous ring homomorphism \(\widehat{R[G]} \to \widehat{R[H...
StageMap
The finite-stage map \(R[G/\varphi^{-1}(V)]\to R[H/V]\) is induced by the continuous homomorphism \(\varphi : G \to H\).
Surjectivity
A surjective continuous homomorphism of profinite groups induces a surjective map on completed group algebras.