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.
Bibliographical noteFunding Information:
I am grateful to Michael Batanin and Clemens Berger for helpful conversations. I also thank the members of the Australian Category Seminar for support and encouragement, and the referee for some remarks on literature sources. This work was supported by an Australian Research Council Postdoctoral Fellowship (project no. DP0558598).