Left Adjoint of Pullback Cat1- profinite groups

Authors : Murat ALP

Pages : 159-168

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :In this paper, we present a brief review crossed modules \cite{whitehead}, cat1-groups \cite{loday}, profinite crossed modules \cite{kortim}, cat1-profinite groups \cite{kortim}, pullback profinite crossed modules \cite{kortim} and also the pullback cat1- profinite groups \cite{hind}. We prove that the pulback cat1-profinite group has a left adjoint which is the induced cat1-group.
Keywords : Crossed modules, Cat1 groups, pullback, Profinite groups, Left, Right Adjoint, Cocomplete category