Crossed modules in the category of cat^1 groups

It is well known that crossed modules over groups are an algebraic model of homotopy 2-type connected spaces. Moreover, cat1-groups and internal categories in the category of groups, i.e. 2-groups or group-groupoids, are categorically equivalent to crossed modules over groups. So these algebraic structures are algebraic models of homotopy 2-type connected spaces. Crossed objects in the category of crossed modules over groups are called crossed squares over groups, and cat1-objects in the category of cat1-groups are called cat2-groups. Crossed squares over groups and the categorically equivalent cat2-groups are an algebraic model of homotopy 3-type connected spaces. In this thesis, as a new algebraic model of homotopy 3-type connected spaces, the algebraic structure of the crossed module on the category of cat1-groups, i.e. the crossed cat1-module, is characterized and some of its properties are studied. It is also shown that such algebraic structures are categorically equivalent to crossed squares over groups.