Left Adjoint of Pullback Cat1 -Groups

In [1] we define the pullback Cat1-groups and showed that the category of pullback Cat1-groups is equivalent to the category of pullback crossed modules. In this paper we proved that the pullback Cat1-group has a left adjoint which is the induced Cat1-group. We also give the left adjoint construction.

Left Adjoint of Pullback Cat1 -Groups

In [1] we define the pullback Cat1-groups and showed that the category of pullback Cat1-groups is equivalent to the category of pullback crossed modules. In this paper we proved that the pullback Cat1-group has a left adjoint which is the induced Cat1-group. We also give the left adjoint construction.