Semistrict models of connected 3-types and Tamsamani’s weak 3-groupoids

Homotopy 3-types can be modelled algebraically by Tamsamani’s weak 3-groupoids as well as, in the path-connected case, by cat²-groups. This paper gives a comparison between the two models in the path-connected case. This leads to two different semistrict algebraic models of connected 3-types using Tamsamani’s model. Both are then related to Gray groupoids.