On cohomological dimensions of totally disconnected locally compact groups

In this paper, we introduce Mackey functors for a t.d.l.c. group and define the cohomological dimension of this group over the Mackey category. We then compare this dimension to the rational discrete cohomological dimension defined by Castellano and Weigel, as well as to the Bredon cohomological dimension of that t.d.l.c. group with respect to the family of compact open subgroups. We also extend results about the geometric dimension of a t.d.l.c. group.