In  we define the pullback Cat^1-groups and showed that the category of pullback Cat^1-groups is equivalent to the category of pullback crossed modules. In this paper we proved that the pullback Cat^1-group has a left adjoint which is the induced Cat^1-group. We also give the left adjoint construction.
ALP, MURAT (1999) "Left Adjoint of Pullback Cat^1 -Groups," Turkish Journal of Mathematics: Vol. 23: No. 2, Article 2. Available at: https://journals.tubitak.gov.tr/math/vol23/iss2/2