  Inspired by work of Szymik and Wahl on the homology of Higman-Thompson
groups, we establish a general connection between ample groupoids, topological
full groups, algebraic K-theory spectra and infinite loop spaces, based on the
construction of small permutative categories of compact open bisections. This
allows us to analyse homological invariants of topological full groups in terms
of homology for ample groupoids.
  Applications include complete rational computations, general vanishing and
acyclicity results for group homology of topological full groups as well as a
proof of Matui's AH-conjecture for all minimal, ample groupoids with
comparison.
